Question

Let R1 be the region in the 1st quadrant bounded by y=x, the y-axis,&the line y=1. Let R2 be the region in the 1st quadrant bounded by y=x2&y=x. Let R3 be the region in the 1st quadrant bounded by y=x2,the x-axis,&the line x=1. Find the volume of the solid generated by revolving R1 about the y-axis.

Answer 1

let try to sketch it first

Answer 2

i have the picture.

Answer 3

\[V =\pi \int\limits_{0}^{1}y^{2} dy\]