Integral Calculus

Find the integral of 12 sin^5 x cos^5 x dx if lower limit = 0 and upper limit = π/2. A. 0.2 B. 0.3 C. 0.4 D. 0.5

A

Find the integral of 12 sin^5 x cos^5 x dx if lower limit = 0 and upper limit = π/2. A. 0.2 B. 0.8 C. 0.6 D. 0.4

A

Find the moment of inertia of the area bounded by the curve x2 = 8y, the line x = 4, and the x-axis on the first quadrant with respect to x-axis. a. 1.52 b. 2.61 c. 1.98 d. 2.36

A

Find the moment of inertia of the area bounded by the curve y2 = 4x, the line x = 1, and the x-axis on the first quadrant with respect to x-axis. a. 1.067 b. 1.142 c. 1.861 d. 1.232

A

Find the moment of inertia with respect to the x axis of the solid generated by revolving the area bounded by y = x2, y = 0 and x = 2 about the x axis a. 256π/9 b. 265π/9 c. 562π/9 d. 652π/9

A

Find the surface area (in square units) generated by rotating the parabola arc y = x2 about the x-axis from x = 0 to x = 1. A. 5.33 B. 4.98 C. 5.73 D. 4.73

A

Find the total length of the curve r = a Cosθ. a. πa b. 2πa c. 1.5πav d. 0.67πa

A

Find the volume of an ellipsoid having the equation 0.04x2 + 0.0625y2 + 0.25z2 = 1. a. 167.55 b. 178.40 c. 171.30 d. 210.20

A

Given is the area in the first quadrant bounded by x2 = 8y, the line, the line x = 4 and the x-axis. What is the volume generated by revolving this area about the y-axis. a. 50.26 m3 b. 52.26 m3 c. 53.26 m3 d. 51.26 m3

A

Integrate the square root of (1 - cosx) dx. A. -2√2cos1/2 x + C B. -2 √2cosx + C C. 2√2 cos1/2 + C D. -2 √2cosx + C

A

Integrate x cos(2x^2 + 7) dx. A. 1/4 sin(2x^2 + 7) + C B. 1/4 cos(2x^2 + 7) + C C. (sin θ)/4(x^2 + 7) + C D. sin(2x^2 + 7) + C

A

Locate the centroid of the area bounded by the curve 5y2 = 16x and y2 = 8x - 24 on the first quadrant. a. (2.20, 1.51) b. (1.50, 0.25) c. (2.78, 1.39) d. (1.64, 0.26)

A

The area enclosed by the ellipse (x2/9) + (y2/4) = 1 is revolved about the line x = 3. What is the volume generated? A. 355.3 cubic units B. 360.1 cubic units C. 370.3 cubic units D. 365.1 cubic units

A

The area on the first and second quadrant of the circle x2 + y2 = 36 is revolved about the line x = 6. What is the volume generated? a. 2131.83 b. 2242.46 c. 2421.36 d. 2342.38

A

The area on the first quadrant of the circle x2 + y2 = 25 is revolved about the line x = 5. What is the volume generated? a. 355.31 b. 365.44 c. 368.33 d. 370.32

A

The following cross section has the following given coordinates. Compute for the centroid of the given cross section. A(2, 2), B(5, 8), C(7, 2), D(2, 0), and E(7, 0). a. (4.6, 3.4) b. (4.8, 2.9) c. (5.2, 3.8) d. (5.3, 4.1)

A

The integral of cos x with respect to x is A. sin x + C B. sec x + C C. -sin x + C D. csc x + C

A

The region in the first quadrant under the curve y = Sinh x from x = 0 to x = 1 is revolved about the x-axis. Compute the volume of solid generated. a. 1.278 m3 b. 2.123 m3 c. 3.156 m3 d. 1.849 m3

A

The region in the first quadrant which is bounded by the curve y2 = 4x, and the lines x = 4 and y = 0, is revolved about the x-axis. Locate the centroid of the resulting solid revolution. a. 2.667 b. 2.333 c. 1.111 d. 1.667

A

What is the area (in square units) bounded by the curve y2 = 4x and x2 = 4y? A. 5.33 sq. units B. 6.67 sq. units C. 7.33 sq. units D. 8.67 sq. units

A

What is the area between y = 0, y = 3x2, x = 0, x - 2? A. 8 sq. units B. 24 sq. units C. 12 sq. units D. 6 sq. units

A

What is the area bounded by the curve y = x3, the x-axis, and the line x = -2 and x = 1? A. 4.25 sq. units B. 2.45 sq. units C. 5.24 sq. units D. 5.42 sq. units

A

What is the integral of (3t - 1)^3 dt? A. 1/12 (3t - 1)^4 + C B. 1/12 (3t - 4)^4 + C C. 1/4 (3t - 1)^4 + C D. 1/4 (3t - 1)^3 + C

A

What is the integral of cos 2x e^sin2x dx? A. e^sin2x /2 + C B. - e^sin2x /2 + C C. -e^sin2x + C D. e^sin2x + C

A

determine the area of the region bounded by the curve y = x^3 - 4x^2 + 3x and the x axis, 0 < x < 3. a. 37/12 b. 36/12 c. 35/12 d. 34/12

A

A triangular section has coordinates of A(2, 2), B(11, 2), and C(5, 8). Find the coordinates of the centroid of the triangular section. a. (7, 4) b. (6, 4) c. (8, 4) d. (9, 4)

B

Determine the area of the region bounded by the curves y = x^4 - x^2 and y = x^2 - 1. a. 9/5 b. 16/5 c. 21/5 d. 27/5

B

Determine the value of the integral of sin5 3x dx with limits from 0 to π/6. A. 0.324 B. 0.178 C. 0.275 D. 0.458

B

Evaluate the integral of (3x^2 + 9y^2) dx day if the interior limit has an upper limit of y and a lower limit of 0, and whose outer limit has an upper limit of 2 and lower limit of 0. A. 10 B. 40 C. 30 D. 20

B

Evaluate the integral of 5cos^6 x sin^2 x dx using lower limit = 0 and upper limit = π/2 A. 0.5046 B. 0.3068 C. 0.6107 D. 0.4105

B

Evaluate the integral of cos x dx limits from π/4 to π/2 A. 0.423 B. 0.293 C. 0.923 D. 0.329

B

Evaluate the integral of ln x dx, the limits are 1 and e. A. 0 B. 1 C. 2 D. 3

B

Evaluate the integral of x cos (4x) dx with lower limit of 0 and upper limit of π/4. A. 1/8 B. -1/8 C. 1/16 D. -1/16

B

Find the area bounded by the parabolas y = 6x - x2 and y = x2 - 2x. Note. The parabolas intersect at points (0, 0) and (4, 8). A. 44/3 sq. units B. 64/3 sq. units C. 74/3 sq. units D. 54/3 sq. units

B

Find the area of the region above the x axis bounded by the function y = 4x - x^2 - 3. a. 1 b. 4/3 c. -4/3 d. -1

B

Find the area of the region bounded by the curves 4x - y^2 = 0 and y = 2x - 4. a. 3 b. 6 c. 9 d. 12

B

Find the area of the region bounded by the parabola y = x^2, the tangent line to the parabola at the point (2,4), and the x axis. a. 1/3 b. 2/3 c. 1 d. 4/3

B

Find the area of the region bounded by y2 = 8x and y = 2x. A. 1.22 sq. units B. 1.33 sq. units C. 1.44 sq. units D. 1.55 sq. units

B

Find the centroid of a right circular cone of altitude h and radius r. a. πr2h/2 b. πr2h/3 c. πr2h/4 d. πr2h

B

Find the centroid of the area bounded by y = 4x - x2 and x + y = 4. a. 3/2 b. 9/2 c. 11/2 d. 14/2

B

Find the coordinates of the centroid of the plane area bounded by the parabola y = 4 - x2 and the x-axis. A. (0, 1) B. (0, 1.6) C. (0, 2) D. (1, 0)

B

Find the length of the arc of the parabola x2 = 4y from x = -2 to x = 2. A. 4.2 units B. 4.6 units C. 4.9 units D. 5.2 units

B

Find the length of the curve having a parametric equations of x = a Cos3θ, y = a Sin2θ from θ = 0° to θ = 2π. a. 5a b. 6a c. 7a d. 8a

B

Find the length of the curve r = 4Sin θ from θ = 0° to θ = 90° and also the total length of curve. a. π ; 2π b. 2π ; 4π c. 3π ; 6π d. 4π ; 8π

B

Find the moment of inertia of the area bounded by the curve x2 = 4y, the line y = 1 and the y-axis on the first axis with respect to y axis. a. 6.33 b. 1.07 c. 0.87 d. 0.94

B

Find the moment of inertia of the area bounded by the curve x2 = 8y, the line x = 4, and the x-axis on the first quadrant with respect to y-axis. a. 21.8 b. 25.6 c. 31.6 d. 36.4

B

Find the moment of inertia of the first quadrant area bounded by y2 = 9x and x = 4 with respect to the x axis a. 476/5 b. 576/5 c. 676/5 d. 776/5

B

Find the moment of inertia with respect to x-axis of the area bounded by the parabola y2 = 4x and the line x = 1. A. 2.03 B. 2.13 C. 2.33 D. 2.53

B

Find the moment of inertia with respect to x-axis of the area bounded by the parabola y2 = 4x, the line x = 1. a. 2.13 b. 2.35 c. 2.68 d. 2.56

B

Find the volume obtained if the region bounded by y = x^2 and y = 2x is rotated about the x axis. a. 64/5 π b. 64/15 π c. 64/19 π d. 64/39 π

B

Find the volume of the solid of revolution formed by rotating the region bounded by the parabola y = x^2 and the lines y = 0 and x = 2 about the x axis a. 29/5 π b. 32/5 π c. 16/5 π d. 2/5 π

B

Given the area in the first quadrant bounded by x2 = 8y, the line x = 4 and the x-axis. What is the volume generated by revolving this area about the y-axis? a. 78.987 m3 b. 50.265 m3 c. 61.253 m3 d. 82.285 m3

B

Locate the centroid of the area bounded by the curve y2 = -1.5(x - 6), the x-axis and the y-axis on the first quadrant. a. (2.2, 1.38) b. (2.4, 1.13) c. (2.8, 0.63) d. (2.6, 0.88)

B

Locate the centroid of the area bounded by the parabolas x2 = 8y and x2 = 16(y - 2) in the first quadrant. a. (3.25, 1.2) b. (2.12, 1.6) c. (2.67, 2.0) d. (2.00, 2.8)

B

Locate the centroid of the plane area bounded by the equation y2 = 4x, x = 1 and the x-axis on the first quadrant. A. (3/4, 3/5) B. (3/5, 3/4) C. (2/3, 3/5) D. (3/5, 2/3)

B

Locate the centroid of the plane area bounded by y = x2 and y = x. A. 0.4 from the x-axis and 0.5 from the y-axis B. 0.5 from the x-axis and 0.4 from the y-axis C. 0.5 from the x-axis and 0.5 from the y-axis D. 0.4 from the x-axis and 0.4 from the y-axis

B

The area bounded by the curve x3 = y, the line y = 8 and the y-axis, is to be revolved about the y-axis. Determine the centroid of the volume generated. a. 4 b. 5 c. 6 d. 7

B

The area bounded by the curve y = x3 and the x-axis. Determine the centroid of the volume generated. a. 2.25 b. 1.75 c. 1.25 d. 0.75

B

The area bounded by the curve y2 = 12x and the line x = 3 is revolved about the line x = 3. What is the volume generated? A. 179 cubic units B. 181 cubic units C. 183 cubic units D. 185 cubic units

B

The area in the second quadrant of the circle x2 + y2 = 36 is revolved about line y + 10 = 0. What is the volume generated? A. 2218.33 cubic units B. 2228.83 cubic units C. 2233.43 cubic units D. 2208.53 cubic units

B

The area in the second quadrant of the circle x2 + y2 = 36 is revolved about the line y + 10 = 0. What is the volume generated? a. 2128.63 b. 2228.83 c. 2233.43 d. 2208.53

B

The area on the first quadrant of the circle x2 + y2 = 36 is revolved about the line y + 10 = 0. What is the volume generated? a. 3924.60 b. 2229.54 c. 2593.45 d. 2696.50

B

The first quadrant area bounded by y2 = 8x, x = 2, and y = 0 is revolved about the x-axis. Find the centroid of the solid generated. a. 8π b. 16π c. 32π d. 64π

B

Using lower limit = 0 and upper limit = π/2, what is the integral of 15sin^7 x dx? A. 6.783 B. 6.857 C. 6.648 D. 6.539

B

What is the area bounded by the curve x2 = -9y and the line y + 1 = 0? A. 3 sq. units B. 4 sq. units C. 5 sq. units D. 6 sq. units

B

A 5 m x 5 cm is cut from a corner of 20 cm x 30 cm cardboard. Find the centroid from the longest side. a. 10.99 m b. 11.42 m c. 10.33 m d. 12.42 m

C

Compute the area of the region bounded by the curve y = 8 - x^2 - 2x and the x axis a. 31 b. 25 c. 36 d. 49

C

Evaluate the double integral of r sin u Dr du, the limits of r is from 0 to cos u and the limits of u is from 0 to π. A. -1/6 B. 1/6 C. 1/3 D. 1/2

C

Evaluate the integral of e^x^2+1 2x dx. A. e^x^2+1 / ln2 + C B. e^2x + C C. e^x^2+1 + C D. 2x e^x + C

C

Evaluate the integral of x(x - 5)^12 dx with limits from 5 to 6. A. 81/182 B. 82/182 C. 83/182 D. 84/182

C

Find the area of the curve r2 = a2cos 2θ. A. a sq. units B. 22 sq. units C. a2 sq. units D. a3 sq. units

C

Find the area of the region bounded by y = x^3 - 3x^2 + 2x + 1, the x axis, and the vertical lines x = 0 and x = 2. a. 0 b. 1 c. 2 d. 3

C

Find the centroid of the area bounded by the curve y = 4 - x2, the line x = 1 and the coordinate axes. a. (0.24, 1.57) b. (1.22, 0.46) c. (0.48, 1.85) d. (2.16, 0.53)

C

Find the length of the curve r = a (1 - Cosθ) from θ = 0° to θ = π and also the total length of the curve. a. 2a ; 4a b. 3a ; 6a c. 4a ; 8a d. 5a ; 9a

C

Find the moment of inertia of the area bounded by the curve x2 = 4y, the line y = 1 and the y-axis on the first quadrant with respect to x-axis. a. 1.2 b. 3.5 c. 0.57 d. 1.14

C

Find the moment of inertia of the area bounded by the curve y2 = 4x, the line x = 1, and the x-axis on the first quadrant with respect to y-axis. a. 0.436 b. 0.682 c. 0.571 d. 0.716

C

Find the total length of the curve r = 4(1 - Sinθ) from θ = 90° to θ = 270° and also the total perimeter of the curve. a. 12, 24 b. 15, 30 c. 16, 32 d. 18, 36

C

Find the volume (in cubic units) generated by rotating a circle x2 + y2 + 6x + 4y + 12 = 0 about the y-axis. A. 39.48 cubic units B. 47.23 cubic units C. 59.22 cubic units D. 62.11 cubic units

C

Find the volume formed by revolving the hyperbola xy = 6 from x = 2 to x = 4 about the x-axis. a. 23.23 m3 b. 25.53 m3 c. 28.27 m3 d. 30.43 m3

C

Find the volume of a spheroid having equation 0.04x2 + 0.111y2 + 0.111z2 = 1. a. 178.90 b. 184.45 c. 188.50 d. 213.45

C

Find the volume of the solid formed if we rotate the ellipse 0.11x2 + 0.25y2 = 1 about the line 4x + 3y = 20. a. 40 π 2m3 b. 45π2m3 c. 48 π 2m3 d. 53 π 2m3

C

Find the volume of the solid of revolution obtained by revolving the region bounded by y = x - x^2 and the x axis about the x axis a. 1/2 b. π/6 c. π/ 30 d. 2/4

C

Given the area in the first quadrant bounded by x2 = 8y, the line y - 2 = 0 and the y-axis. What is the volume generated when revolved about the line y - 2 = 0? a. 53.31 m3 b. 45.87 m3 c. 26.81 m3 d. 33.98 m3

C

Given the area in the first quadrant bounded by x2 = 8y, the line y - 2 = 0 and the y-axis. What is the volume generated when this area is revolved about the x-axis. a. 20.32 m3 b. 34.45 m3 c. 40.21 m3 d. 45.56 m3

C

Integrate (7x^3 + 4x^2) dx. A. 7x^3/3 + 4x^2/2 + C B. 7x^4/4 + 4x^2/5 + C C. 7x^4/4 + 4x^3/3 + C D. 7x^4 + 4x/2 + C

C

Locate the centroid of the area bounded by the parabola y2 = 4x, the line y = 4 and the y-axis. a. (0.4, 3) b. (0.6, 3) c. (1.2, 3) d. (1.33, 3)

C

Sections ABCD is a quadrilateral having the given coordinates A(2, 3), B(8, 9), C(11, 3), and D(11, 0). Compute for the coordinates of the centroid of the quadrilateral. a. (5.32, 3) b. (6.23, 4) c. (7.33, 4) d. (8.21, 3)

C

The area bounded by the curve y2 = 12x and the line x = 3 is revolved about the line x = 3. What is the volume generated? a. 185 b. 187 c. 181 d. 183

C

The area enclosed by the curve 9x2 + 16y2 = 144 on the first quadrant, is revolved about the y-axis. What is the volume generated? a. 98.60 b. 200.98 c. 100.67 d. 54.80

C

The area enclosed by the ellipse 0.11x2 + 0.25y2 = 1 is revolved about the line x = 3, what is the volume generated? a. 370.3 b. 360.1 c. 355.3 d. 365.1

C

The area of the second and third quadrant of the circle x2 + y2 = 36 is revolved about the line x = 4. What is the volume generated? a. 2320.30 b. 2545.34 c. 2327.25 d. 2520.40

C

What is the area (in square units) bounded by the curve y2 = x and the line x - 4 = 0? A. 30/3 sq. units B. 31/3 sq. units C. 32/3 sq. units D. 29/3 sq. units

C

What is the integral of sin^5 x cos^3 x dx if the lower limit is zero and the upper limit is π/2? A. 0.0203 B. 0.0307 C. 0.0417 D. 0.0543

C

A body moves such that its acceleration as a function of time is a = 2 + 12t, where "t" is in minutes and "a" is in m/min^2. Its velocity after 1 minute is 11 m/min. Find distance traveled after 4 minutes. A. 135 m B. 186 m C. 121 m D. 156 m

D

A hole of radius 2 is drilled through the axis of a sphere of radius 3. Compute the volume of the remaining solid. a. 12π√5 /3 b. 15π√5 /3 c. 18π√5 /3 d. 20π√5 /3

D

Compute the volume of the solid obtained by rotating the region bounded by y = x^2, y = 8 - x^2, and the y axis about the x axis. a. 103/3 π b. 157/3 π c. 236/3 π d. 256/3 π

D

Derive a formula for the volume of a sphere of radius r by rotating the semicircle y = √r^2 - x^2 about the x axis a. 4/3 π^2 b. 4/3 π^3 c. 4/3 πr^2 d. 4/3 πr^3

D

Evaluate the double integral of r sin u dr du, the limits of r is 0 and cos u and the limit of u are 0 and pi. A. 1 B. 1/2 C. 0 D. 1/3

D

Evaluate the integral of (3x2 + 9y2) dx dy if the interior limits has an upper limit of y and a lower limit of 0, and whose outer limit has an upper limit of 2 and a lower limit of 0. A. 10 B. 20 C. 30 D. 40

D

Evaluate the integral of dx/(x + 2) from -6 to -10. A. 2^1/2 B. 1/2 C. ln 3 D. ln 2

D

Evaluate the integral of sin^6 x dx from 0 to π/2. A. π/32 B. 2π/17 C. 3π/32 D. 5π/32

D

Evaluate the integral of xsin2x dx. A. -x/4 cos2x + 1/2 sin2x + C B. -x/2 cos2x - 1/4 sin2x + C C. x/4 cos2x - 1/2 sin2x + C D. -x/2 cos2x + 1/4 sin2x + C

D

Find the area (in sq. units) bounded by the parabolas x2 - 2y = 0 and x2 + 2y - 8 = 0. A. 11.77 sq. units B. 4.7 sq. units C. 9.7 sq. units D. 10.7 sq. units

D

Find the area enclosed by the curve x2 + 8y + 16 = 0, the x-axis, the y-axis and the line x - 0. A. 7.67 sq. units B. 8.67 sq. units C. 9.67 sq. units D. 10.67 sq. units

D

Find the area in the first quadrant bounded by the parabola y2 = 4x, x = 1, and x = 3. A. 9.555 sq. units B. 9.955 sq. units C. 5.955 sq. units D. 5.595 sq. units

D

Find the area of the region bounded by y = x^2 - 5x + 6, the x axis, and the vertical lines x = 0 and x = 4. a. 14/3 b. 15/3 c. 16/3 d. 17/3

D

Find the centroid of the area bounded by the curve x2 = -(y - 4), the x-axis and the y-axis on the first quadrant. a. (0.25, 1.8) b. (1.25, 1.4) c. (1.75, 1.2) d. (0.75, 1.6)

D

Find the integral of [(ex - 1) / (ex + 1)] dx A. ln (ex - 1)2 + x + C B. ln (ex + 1) - x + C C. ln (ex - 1) + x + C D. ln (ex + 1)2 - x + C

D

Find the moment of inertia of a rectangle with respect to its base. a. b3d/3 b. bd3/3 c. b3h/3 d. bh3/3

D

Find the moment of inertia of a right circular cylinder with respect to its axis. a. πH4R/2 b. πHR3/2 c. πH3R/2 d. πHR4/2

D

Find the moment of inertia of the area bounded by the curve y2 = 4x, the line y = 2, and the y-axis on the first quadrant with respect to y-axis. a. 0.064 b. 0.076 c. 0.088 d. 0.095

D

Find the volume common to the cylinders x2 + y2 = 9 and y2 + z2 = 9. a. 241 m3 b. 533 m3 c. 424 m3 d. 144 m3

D

Find the volume obtained if the region bounded by y = x^2 and y = 2x is rotated about the x axis a. 63/15 π b. 61/15 π c. 62/15 π d. 64/15 π

D

Given the area in the first quadrant bounded by x2 = 8y, the line y - 2 = 0 and the y-axis. What is the volume generated when the area is revolved about the line y - 2 = 0? A. 28.41 cubic units B. 27.32 cubic units C. 25.83 cubic units D. 26.81 cubic units

D

Given the area in the first quadrant by x2 = 8y, the line x = 4 and the x-axis. What is the volume generated by revolving this area about the y-axis. A. 53.26 cubic units B. 52.26 cubic units C. 51.26 cubic units D. 50.26 cubic units

D

Integrate 1/3x + 4 with respect to x and evaluate the result from x = 0 and x = 2. A. 0.278 B. 0.336 C. 0.252 D. 0.305

D

The area enclosed by the ellipse 0.0625x2 + 0.1111y2 = 1 on the first and 2nd quadrant, is revolved about the x-axis. What is the volume generated? a. 151.40 b. 155.39 c. 156.30 d. 150.41

D

The region in the first quadrant, which is bounded by the curve x2 = 4y, the line x = 4, is revolved about the line x = 4. Locate the centroid of the resulting solid revolution. a. 0.6 b. 0.5 c. 1.0 d. 0.8

D

What is the area bounded by the curve y2 = x and the line x - 4 = 0? A. 11 sq. units B. 31/3 sq. units C. 10 sq. units D. 32/3 sq. units

D

What is the integral of sin^5 x dx if the lower limit is 0 and the upper limit is π/2? A. 0.233 B. 0.333 C. 0.433 D. 0.533

D

A cross section consists of a triangle and a semi circle with AC as its diameter. If the coordinates of A(2, 6), B(11, 9), and C(14, 6). Compute for the coordinates of the centroid of the cross section. a. (4.6, 3.4) b. (4.8, 2.9) c. (5.2, 3.8) d. (5.3, 4.1)

A

A square hole of side 2 cm is chiseled perpendicular to the side of a cylindrical post of radius 2 cm. If the axis of the hole is going to be along the diameter of the circular section of the post, find the volume cutoff. a. 15.3 m3 b. 23.8 m3 c. 43.7 m3 d. 16.4 m3

A

Determine the area of the region bounded by the parabola y = 9 - x^2 and the line x + y = 7. a. 9/2 b. 1/3 c. 8/3 d. 7/6

A

Evaluate the integral cos^8 3A dA from 0 to π/6. A. 35π/768 B. 23π/765 C. 27π/363 D. 12π/81

A

Evaluate the integral of 3 (sin x)^3 dx using lower limit of 0 and upper limit= π/2. A. 2.0 B. 1.7 C. 1.4 D. 2.3

A

Evaluate the integral of xcos2x dx with limits from 0 to π/4. A. 0.143 B. 0.258 C. 0.114 D. 0.186

A

Evaluate the integral of xdx/(x+1)^8 if it has an upper limit of 1 and a lower limit of 0. A. 0.022 B. 0.056 C. 0.043 D. 0.031

A

Find the Centroid of the area under the curve y = x2 from x = 2 to x = 4. a. 56/3 b. 65/3 c. 63/3 d. 36/3

A

Find the area bounded by the curve y = x2 + 2 and the lines x = 0 and y = 0 and x = 4. A. 88/3 sq. units B. 64/3 sq. units C. 54/3 sq. units D. 64/5 sq. units

A

Find the area bounded by the line x - 2y + 10 = 0, the x-axis, the y-axis and x = 10. A. 75 sq. units B. 50 sq. units C. 100 sq. units D. 25 sq. units

A

Find the area bounded by the parabola x2 = 4y and y = 4. A. 21.33 sq. units B. 33.21 sq. units C. 31.32 sq. units D. 13.23 sq. units

A

Find the area of the region bounded by the curve y = x^3 and the line y = 8 using (a) vertical rectangles and (b) horizontal rectangles. a. 12 b. 9 c. 6 d. 3

A

Find the area of the region bounded by the parabola x = y^2 and the line y = x - 2. a.

A

Find the centroid of the area bounded by r = 3secθ, θ = 0 and θ = π/3

A

Find the centroid of the area in first quadrant bounded by the curve y2 = 4ax and the latus rectum. a. (0.6a, 0.75a) b. (1.23a, 0.95a) c. (0.94a, 2.97a) d. (1.16a, 0.53a)

A

Find the centroid of the area under y = 4 - x2 in the first quadrant. a. (0.75, 1.6) b. (1.6, 0.95) c. (0.74, 1.97) d. (3.16, 2.53)

A

Find the double integration the centroid of the area bounded by y2 = x and x2 = 8y. a. 8/3 b. 11/3 c. 17/3 d. 22/3

A