Given that ∫ dx/(x^2+4) = 1/2 tan-1 x/2 +C
a. If t=tanx show that dx/dt= 1/(1+t^2)
b. Hence evaluate ∫ dx/(1+3cos^2x)
數學integration
2011-12-10 9:43 pm
回答 (1)
2011-12-10 10:47 pm
✔ 最佳答案
t = tanxdt = dtanx = (secx)^2 dx
dx/dt = 1/(secx)^2 = 1/(1 + t^2)
(b) ∫ 1/(1+ 3(cosx)^2) dx
= ∫ (cscx)^2 /((cscx)^2+ 3(cotx)^2) dx
= - ∫ 1 /((cscx)^2+ 3(cotx)^2) d(cotx)
= - ∫ 1 /(1+ 4(cotx)^2) d(cotx)
= -(1/2)arctan(2cot(x)) + C
收錄日期: 2021-04-26 19:16:55
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20111210000051KK00327