Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 9 sin(x), y = 9 cos(x), 0 ≤ x ≤ 𝜋/4; about y = −1

Answer 1

By Disk method V = π∫₀^π/4[(9cosx + 1)² - (9sinx + 1)]dx = π∫₀^π/4(81cos2x + 18cosx - 18sinx)dx =

π(81sin2x/2 + 18sinx + 18cosx)₀^π/4 = π[(81/2 + 9√2 + 9√2) - 18] = π(45/2 + 18√2) = 150.658