Method of disk (in respect to y)

[jwxie]

Homework Statement

Revolve the region under the curve y =√x on the interval [0, 4] about the x-axis and
find the volume of the resulting solid of revolution.

YET, NOW, I want to do in respect to y

Homework Equations

integral formula

The Attempt at a Solution

I did dx and I got 8pi which is corrected.

So I decided to do it with dy.

I looked at the graph and I saw the height would be the same (well because of the problem's nature). so a and b will stay the same

integral of pi*r^2
we know r is y^2 (since y^2 = x)
integral of pi * (y^2)^2 from 1 to 4

but I did not get 8pi
why?

thanks.

 

[rock.freak667]

The integral you evaluated, gives the volume when the curve is rotated about the y-axis, not the x-axis.

 

[jwxie]

The original function was y = sqrt of x
so inverse it, we got x = y^2

you were right about the fact. i think the point of a and b should be 0 to 2, since y^2 = x, so (2^2) = 4

integral of pi * (y^2)^2 from 0 to 2
but i got 16/5 instead