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

Question

y = (64 − x^2)^(1/4), y = 0, x = 6, x = 7; about the x-axis

Answer 1

v = ∫[6,7] πr^2 dx
where r = y = ∜(64-x^2)

v = π∫[6,7] √(64-x^2) dx
= π(1/2 √(64-x^2) + 32 arcsin(x/8)) [6,7]
= π(√15/2 - √7 + 32(arcsin(7/8)-arcsin(3/4)))