Thread: finding volume by the washer method

I have a few problems I'm trying to solve and could use some help on


1) y=4-x^2, y=2-x (rotate about the x axis)

So my inner radius is 2-x, my outer radius is 4-x^2

I integrate from x=-1 to x=3 because that's where they intersect.

So I integrate:

pi(4-x^2)^2 - pi(2-x)^2 which comes out to

48pi - pi4^5/5 + 64pi/3

2) y= secx, y=tanx, x=0, x=1
Integrate from 0 to 1, rotate about x axis
Inner radius is tanx, outer is secx.

So I have to integrate
pi(secx)^2 - pi(tanx)^2 = pisec^2x - pitan^2x =

pi integral sec^2x-sec^2x-1 = -pi(x)


3)y=2x, y=0, x = 1 (thus x=y/2)
Rotate about the line x=1

outside radius = 1-y/2

integratee pi(1-y/2)^2 which comes out to 2/3pi

Then I have to do the same shape, but with a different radius (about the line x=2 and limits of integration... so I figure if that one is right then the next one will be too.)

you have the right idea on all of them however you may want to consider

the shell method on #3

Ok great.

We haven't covered the shell method yet though? My professor mentioned it but didn't go into depth on it yet.