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求不定积分,上限为π,下限为0,根号下(sint-sint的立方)dt,
人气:408 ℃ 时间:2019-08-21 10:44:27
解答
是求定积分!
I=∫√[sint-(sint)^3]dt=∫√{sint[1-(sint)2]}dt
=∫|cost|√sintdt
=∫cost√sintdt+∫(-cost)√sintdt
=∫√sintdsint-∫√sintdsint
=[(2/3)(sint)^(3/2)]-[(2/3)(sint)^(3/2)]
=2/3-(-2/3)=4/3.
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