積分積分積分積分積分積分~~~

圖片參考：http://imgcld.yimg.com/8/n/AE03435620/o/150912270102113872056060.jpg

The answer is
if a=b, divergent else 0

Ps.記得已回答,怎不見了?



2009-12-27 18:34:36 補充：
Sorry!正更如下:
pi/b - (a-b)pi/[b(a+b)]= b*pi/(a+b)

2009-12-27 19:03:13 補充：
最後一行寫錯了!更正
if (a (A)=π/b - [2(a²-b²)/b]*[1/(a-b)^2]*[(a-b)/(a+b)]*(-π/2) = π
if (a>b) =>(A)=π/b - [2(a²-b²)/b]*[1/(a-b)^2]*[(a-b)/(a+b)]*(π/2) = 0

2009-12-27 19:56:03 補充：
考慮a,b可能有正負號: arctan[(a-b)/(a+b)]=arctan[(a²-b²)/(a+b)²]
故a² > b² 時為 π/b - π/b =0
a² < b² 時為 π/b + π/b = 2π/b

到下面的網址看看吧

▶▶http://qaz331.pixnet.net/blog

有沒有那麼醜...
how?

x/(2 b) + ArcTan[((a + b) Cos[x/2])/(a Sin[x/2] - b Sin[x/2])]/(2 b) -
ArcTan[((a + b) Cos[x/2])/(-a Sin[x/2] + b Sin[x/2])]/(2 b)