Set up the integral that uses the method of disks/washers to find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified lines.

Question

Y=3√x, y=3x

a) about the y-axis

b) about the line y=3

Answer 1

a) V= π ∫ [R²(y) - r²(y)] dy, where R(y) = y/3 and r(y) = y²/9 ∫ is from 0 to 3

After calculations V = π 12/5

b) V= π ∫ [R²(x) - r²(x)] dx, where R(x) = 3 - 3x, r(x) = 3 - √x; ∫ is from 0 to 1

After calculations V = π 3/2