作者Eliphalet (信我，会很劲的)
站内trans_math
标题Re: [积分] 求积分
时间Fri Jan 2 08:59:15 2009
※ 引述《biggerlin (比格)》之铭言：
: 以下几题，求积分值
: 麻烦请写出计算过程，或是有hint吗?
: 谢谢
: (π/2) dx
: (c)∫ ───────
: (π/3) 1+sinx+cosx
1 1
------------------------ = ---------------------------------------------
1 + sin(x) + cos(x) 2 * sin(x/2) * cos(x/2) + 2 * (cos(x/2))^2
(sec(x/2))^2
= --------------------------
2 [ 1 + tan(x/2)]
π/2 dx
=> ∫ ------------------------
π/3 1 + sin(x) + cos(x)
π/2
= ln [ tan(x/2) + 1 ] |
π/3
= ln 2 - ln(1 + √3 / 3 )
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1F：推 biggerlin:感谢! 61.228.197.93 01/02 23:06