求(1—sinx三次方)的定积分,积分上限是π,积分下限是0

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求(1—sinx三次方)的定积分,积分上限是π,积分下限是0

求(1—sinx三次方)的定积分,积分上限是π,积分下限是0
求(1—sinx三次方)的定积分,积分上限是π,积分下限是0

求(1—sinx三次方)的定积分,积分上限是π,积分下限是0
∫(0→π) (1 - sin³x) dx
= ∫(0→π) dx - ∫(0→π) sin³x dx
= [ x ] |(0→π) + ∫(0→π) (1 - cos²x) d(cosx)
= π + [ (cosx - 1/3 * cos³x) ] |(0→π)
= π + [(- 1) - (1/3)(- 1)] - [(1) - (1/3)(1)]
= π - 4/3