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## 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.