Calculus Ch 4

Find the indefinite integral and check your result by differentiation. (Use C for the constant of integration.) 1. (4 cos(x) + 9 sin(x)) dx 2. t^3 − cos(t)dt 3. 2(sec(x))^2 - 9(sin(x))dx 4. csc(y)^2 - sec(y)tan(y)dy 5. (sec^2y - siny) dy 6. (tany^2 +1)dy 7. (1- cscycoty)

1. 4sinx -9cosx + C 2. 1/4t^4 - sint + C 3. 2(sin/cos) + 9cos + C 4. −cot(y) − sec(y) + C 5. tany + cosy + y 6. tany + C 7. y + cscy + C

Find the indefinite integral and check your result by differentiation. (Use C for the constant of integration.) 1. (5-x)dx 2. (5x-8x^2)dx 3. (x^3/2+12x+2)dx 4. 6th root of (x^5) +5 5. x+8 / sqrt of x 6. y^4 x sqrt of y 7. 1 / x^5 8. dy 9. -7dt

1. 5x - 1/2 x^2 + C 2. 5/2 x^2 - 8/3 x^3 + C 3. 2/5 x^5/2 + 6x^2 + 2x + C 4. 6/11 x^11/6 + 5x + C 5. 2/3x^3/2 + 16sqrtx + C 6. 2/11y^11/2 + C 7. -1/4x^4 + C 8. y + C 9. -7t + C

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your result. 1. 5 8dv 4 2. 8 (-5v +5)dv 3 3. 3 (4t-1)^2 dt 0

1. 8 2. -225/2 3. 111

Find a function f that satisfies the conditions. f ''(x) = x^2 f '(0) = 7 f(0) = 9

1/12 X^4 + 7x + 9

2 x/4 dx 0

1/2

Evaluate the definite integral by the limit definition. 3 7x^2 dx 1

182/3

4 4x^2 dx 1

84

Solve the differential equation. f''(x)= 4 f'(2)= 13 f(2)=19

f(x)=2x^2 + 5x + 1

Find the particular solution that satisfies the differential equation and the initial condition h'(t)= 8t^3 + 5 h'(1) = -4

h(t)= 2t^4 +5t - 11