∫√(9-4X^2) dX
please show the steps~
一題好easy既indefinite integral
2011-05-05 5:14 am
回答 (1)
2011-05-05 5:35 am
✔ 最佳答案
∫ √(9 - 4x^2) dx= 3 ∫ √(1 - [(2/3)x^2]) dx
Let (2/3)x = siny, dx = (3/2)(cosy)
= (9/2) ∫ (cosy)^2 dy
= (9/2) ∫ (1 + cos2y)/2 dy
= (9/4)(y + sin2y) + C
= (9/4)arcsin[(2/3)x] + (1/2)√(9 - 4x^2) + C
收錄日期: 2021-04-26 14:07:31
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110504000051KK01077