Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, x = y2; about y = 1

We have y = 22
D? y
= VE
Now we find the points of intersection first: 27?
-
VE
2 = 0, 1 so when x is O y is also 0
and when x is 1, y is also 1
Hence the points of intersection are (0,0) and (1,1)
Given it is rotated about y
=1
So using disk method, the volume is given by:

The answer is 26 to 1