Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=0, y=cos(5x), x=pi/10 , x= 0, about the axis y=-1

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(5x), x=pi/10 , x= 0, about the axis y=-1

Answer 1

desmos.com/calculator/olpkqqs0xh

Answer 2

corrected V_t from (2π/5)3+3π²/10 to (2π/)+3π²/20

answer now matches other answer given.

the volume differential for the solid and the cylinder of r=1 is

dV_t=π(cos5x+1)²dx

use cos²5x=(1/2)(1+cos10x)]after integrating find

V_t=π[[sin(10x)]/20+(2/5)sin(5x)+3x/2],,,,evaluated x=0 to π/10

which is V_t=(2π/5)+3π²/20

the volume for the cylinder r=1 is

V_c=π²/10=2π²/20

V_s=V_t-V_c