Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Given a diagram from Calculus of a Single Variable by Larson and Edward (9th edition):

enter image description here

I am interested in finding the volume of various regions when rotated about various lines. Specifically, I am wondering if my set-up for finding the volume is correct; I have no issues simply integrating such functions. Note that this is not homework - I am just reviewing for an exam tomorrow.

Problem 1: $R_3$ about $x = 1$

I used a horizontal slice (disk), so my integral was $$\pi\int_0^1 (1-\sqrt{y})^2 dy$$ since every part of of the region $R_3$ is touching the axis of revolution.

Problem 2: $R_2$ about $x = 1$

Again, I used a horizontal slice, except this one was a washer. My integral was $$\pi\int_0^1 (1-y)^2 - (1-\sqrt{y})^2 dy$$

Just looking for a confirmation that this or correct or (if needed) an explanation of why I am wrong. Thanks.

share|improve this question
    
For problem 2, check the outer radius expression in the integrand. –  David Mitra Apr 27 '12 at 2:04
    
Ah, the outer radius is always at a distance $y$. My inner radius is still fine though, correct? –  Joe Apr 27 '12 at 2:07
    
Yes.${}{}{}{}{}$ –  David Mitra Apr 27 '12 at 2:08
    
@DavidMitra Thanks for the quick responses. –  Joe Apr 27 '12 at 2:08
1  
click me –  David Mitra Apr 27 '12 at 2:13
show 2 more comments

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.