Question

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

y = √(x-1), y = 0, x= 5;
about the line y = 3.

Answer 1

(1/3)π(5-1)^3

Explanation:

The volume of the solid obtained by rotating the region bounded by the given curves about the specified line, y = 3, is

V = ∫5√(x-1) dx

V = ∫5(y-(-1)) dy

V = ∫5(y+1) dy

V = ∫5y dy + ∫5dy

V = ∫5y dy + 5

V = [y^2/2]5 + 5

V = [5^2/2] + 5

V = 5+5

V = 10