OU Calculus II w/ Blake Regan Exam 2

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 4 − (1/2)x, y = 0, x = 0, x = 1; about the x-axis

169pi/12

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 9x^5, y = 9x, x ≥ 0; about the x-axis

216pi/11

A variable force of 4x−2 pounds moves an object along a straight line when it is x feet from the origin. Calculate the work done in moving the object from x = 1 ft to x = 15 ft. (Round your answer to two decimal places.)

3.73

Find the volume V of the described solid S. The base of S is an elliptical region with boundary curve 9x2 + 16y2 = 144. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.

48

Consider the solid obtained by rotating the region bounded by the given curves about the line x = 3. x= 3 y^2 , x = 3 Find the volume V of this solid.

48pi/5

Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y = 1/x, x = 1, x = 8, y = 0 Find the volume V of this solid.

7pi/8

Suppose that 3 J of work is needed to stretch a spring from its natural length of 32 cm to a length of 49 cm. (a) How much work is needed to stretch the spring from 36 cm to 41 cm? (Round your answer to two decimal places.) (b) How far beyond its natural length will a force of 45 N keep the spring stretched? (Round your answer one decimal place.)

a.) 0.67 b.) 21.68 cm

Find the solution of the differential equation that satisfies the given initial condition. dy/dx = x/y , y(0) = −5

y = -sqrt[x^2 +25]

Solve the differential equation. (Use C for any needed constant.) xy2y' = x + 6

y=3√3x+18ln|x|+C

Solve the differential equation. (Use C for any needed constant.) dz/dt + 4e^(t + z) = 0

(1/4e^z) = e^t +C

Find the centroid of the region bounded by the given curves. x = 5 − y2, x = 0

(2,0)

Solve the differential equation. (Use C for any needed constant.) 4(dy/dθ) = [e^y sin^2 (θ)] / [y sec θ]

-4ye^-y - 4e^-y = (1/3) sin^3 (theta) +C