Solve Volume Problem: Find Region Bounded by Line & Curve

[chesshaha]

Homework Statement

Find the volume of the soild formed.
The region bounded by the line y=x, and the curve y=x^2. about the line x=1

Homework Equations

Either Washer or Shell

The Attempt at a Solution

I want to use washer, but have to switch to dy.
I want to use shell, but don't think it will work.

I don't think this is right, but here is what I have.

integral of pie[(1-y^(1/2))-(1-y)]dy from 0 to 1.

Thanks, please help.

 

[eigenglue]

Ok for a washer the area is pie(r1^2 - r2^2), where r1 is the larger radius and r2 is the smaller radius. So I think you just need to take a closer look at which is the larger and smaller radius and remember to square them too.

OTOH if you used shells you might not have to deal with a square root term in your integral.

 

[chesshaha]

the about x=1 is what mess me up. i meant to spuare all the R's but forgot, because this is hard to see.

integral of pie[(1-y)^2-(1-y^(1/2))^2]dy from 0 to 1.

this is right now?

I got pi/6, it looks right, but is it?

 

[Dick]

Looks correct to me.