Question

find the volume using the disc method
f(x)=5sin(x) between x=0 and x=pie

Answer 1

Assuming the curve y = 5 sin x is revolved about the x-axis from x = 0 to x = π, the disc method gives

V = π ∫_0^π [5 sin x]^2 dx = 25π ∫_0^π sin^2 x dx.

Use sin^2 x = (1 − cos 2x)/2:

V = 25π ∫_0^π (1 − cos 2x)/2 dx
= (25π/2) [x − (sin 2x)/2]_0^π
= (25π/2) (π − 0)
= 25π^2 / 2.

Numerically, V ≈ 123.37.