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∫1(上标)-1(下标)√(1-x²)dx=?
人气:129 ℃ 时间:2019-12-06 20:09:55
解答
设x=sin⁡t,因此(-π/2≤t≤π/2)
则原式变为∫_(-π/2)^(π/2)▒cos⁡t d_sin⁡t =∫_(-π/2)^(π/2)▒〖(cos⁡t )^2 〗 d_t
=∫_(π/(-2))^(π/2)▒(1+cos⁡2t)/2 d_t
=(t/2+sin⁡2t/4)|_((-π)/2)^(π/2)
=π/2
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