旋转体体积
= ∫[0→π] 2πxy dx
= 2π∫[0→π] xsinx dx
= 2π∫[0→π] x d[- cosx]
= - 2πxcosx |[0→π] + 2π∫[0→π] cosx dx
= - 2π[π(- 1) - 0] + 2π[sinx] |[0→π]
= 2π²
旋转体体积
= ∫[0→π] 2πxy dx
= 2π∫[0→π] xsinx dx
= 2π∫[0→π] x d[- cosx]
= - 2πxcosx |[0→π] + 2π∫[0→π] cosx dx
= - 2π[π(- 1) - 0] + 2π[sinx] |[0→π]
= 2π²