[積分] 疑問
√X
∫ --------- dx
√(1-X)
√X * √X
=∫ ---------------- dx
√(1-X) * √X
X
=∫ ------------------dx
√(X-X^2)
X
=∫ --------------------------------- dx
√( (1/4) +[(-1/4) +X -X^2])
X
=∫ --------------------------- dx ( let x-1/2 =(1/2)sinΘ) ==> sinΘ=2x-1
√ ((1/4) - (X-(1/2))^2) ( dx =(1/2)cosΘ) Θ=sin^(-1)(2x-1)
(1/2) +(1/2)sinΘ
=∫ --------------------------- (1/2) cos ΘdΘ
(1/2) cos Θ
=∫ (1/2) +(1/2)sinΘ dΘ
= (1/2)Θ -(1/2)cosΘ + c
=(1/2)sin^(-1)(2x-1) -(1/2) √(1-(2x-1)^2) +c
請問那邊算錯可以幫忙檢查媽 ?
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◆ From: 140.115.213.118
推
192.192.12.186 03/21, , 1F
192.192.12.186 03/21, 1F
如果令 √X =sinΘ
答案會不一樣~~
所以~~那個對~~還是都對?
※ 編輯: youyouyou 來自: 140.115.213.118 (03/21 18:41)
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