Which of the following integrals represents the volume of the solid obtained by rotating the region bounded by the curves 𝑦=sin(𝑥) and 𝑦=0, with 0≤𝑥≤𝜋 about the line 𝑦=1?

Question

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Answer 1

Volume v = π∫₀^π[1 - (1 - sinx)²]dx = π∫₀^π(2sinx - sin²x)dx = π(- 2cosx - 1/2x + 1/4sin2x)₀^π= π[(2 - π/2) - (- 2)] = π(4 - π/2)