作者Frobenius (▽．(▽×▽φ)=0)
看板Math
标题Re: [微积] sin躲在cos里面!
时间Wed Jun 8 23:51:19 2011
※ 引述《lowpitch (chia)》之铭言：
: 小弟不才，写习题遇到一个积分做不出来
: 经简化不影响整体概念式子如下
: S cos(ksinx)dx
: 上下界是正负二分之pi
: k为一常数
: 婐可爱的计算机告诉我无论k是多少
: 结果都是pi!!!
: 许多想法都失败上板求高手解答...
By Mathematica 7.0
Integrate[Cos[k Sin[x]], {x, -\[Pi]/2, \[Pi]/2}]
If[k \[Element] Reals, \[Pi] BesselJ[0, Abs[k]],
Integrate[Cos[k Sin[x]], {x, -(\[Pi]/2), \[Pi]/2},
Assumptions -> k \[NotElement] Reals]]
Integrate[Cos[k Sin[x]], {x, -\[Pi]/2, \[Pi]/2},
GenerateConditions -> False]
\[Pi] BesselJ[0, k]
π/2
∫ cos(ksinx) dx = π BesselJ (|k|)
-π/2 0
π/2
∫ cos(0sinx) dx = π BesselJ (|0|) = π
-π/2 0
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