The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.

Question

y = −x^2 + 14x − 45, y = 0; about the x-axis

Answer 1

the curve intersects y=0 at x=5,9

v = ∫[5,9] π (−x^2 + 14x − 45)^2 dx
= π (x^5/5 - 7x^4 + 286/3 x^3 - 630x^2 + 2025x [5,9]
= 512/15 π