Math 1508

Quiz Number 2
Feb. 2, 1997

Problem 1 (10 points)

1. Find the volume generated by taking the area in the 1st quadrant bounded by the
line y=x and the curve y = x^5 and rotating about the line x = 2.

ans

This can written x = y and x = y^(1/5)

Plot[{x,x^5},{x,-.5,3}]

Washers. Integrate with respect to y from 0 to 1.
Outside diameter

od = 2 -y

id = 2 - y^(1/5)

Integrate[Pi (od^2 - id^2), {y,0,1}]

Problem 2: (10 points)

Same as problem one but rotated about the line y = -1.

ans

Plot[{x,x^5},{x,-1,3}]

Washers, integrate wrt x

Problem 3 (5 points)

Find the length of the curve 6 x^(3/2) -2 from x = 0 to x = 1. Just set up the integral do not evaluate.

ans

This is what you integrate. You integrate it from 0 to 1. The actual problem STOPS HERE.