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.Write an integral expression for the volume of the slid described. The volume of the solid generated by revolving R1 about the line y-axis.

Answer 1

This is a cone with height 1 and radius 1.\[V=\frac{1}{3}\pi.\]

Answer 2

i need an expression...

Answer 3

\[\pi \int\limits_{0}^{1}x ^{2}dx\]

Answer 4

Fine...\[V=\pi\int_{0}^{1}x^2dx=\frac{1}{3}\pi.\]

Answer 5

But I think it helps better to think about it.