finding volume of the below question

Question

Find the volume bounded by z= 2x, z= y, inside x^2 + y^2 =1 above the xy-plane.

Answer 1

It's a plane cutting through the circular cylinder of radius 1 at an angle. The integral is

Int in x from 0 to 1 of Int in y from -sqrt(1-x²) to sqrt(1-x²) of int in z from 0 to 2x dzdydx.

This ends up as integral from 0 to 1 of 2(1-x²) dx = 4/3

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