finding the volume of the solid obtained by rotating the region bounded by the given curves

Question

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.y=0,y=cos(7x),x=π/14,x=0 about the axis y=−8

Answer 1

By Disk Method volume V = π∫₀^π/14(cos(7x) + 8)²dx = π∫₀¹⁴(64 + 16cos(7x) + cos²(7x))dx = π∫₀¹⁴(64.5 + 16cos(7x) + 1/2cos(14x))dx = π(64.5x + 16/7sin(7x) + 1/28sin(14x))₀^π/14 = π(64.5·π/14 + 16/7) = 52.65

Answer 2

The washer method: integral from x = 0, π/14 of π((y+8)² - 8²)dx where first term is r_outer² and the second is r_inner²