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How to integrate cos( sin(x) ) from 0 to pi

  • Thread starter dirk_mec1
  • Start date
  • #1
761
13

Homework Statement



[tex]
\int_{0}^{\pi} \cos ( \sin x ) \mbox{d}x
[/tex]




The Attempt at a Solution



If I use [itex]u = \pi-x [/itex] I get :



[tex]
\int_{0}^{\pi} \cos ( \sin x ) \mbox{d}x = \int_{0}^{\pi} \sin ( \cos x ) \mbox{d}x
[/tex]

but then what?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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That reminds me of a definition of the Bessel function in terms of integrals...
 
  • #3
761
13


So n = 0 here:

[tex] J_n(x) = \frac{1}{\pi} \int_{0}^{\pi} \cos (n \tau - x \sin \tau) \,\mathrm{d}\tau. [/tex]
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618


So n = 0 here:

[tex] J_n(x) = \frac{1}{\pi} \int_{0}^{\pi} \cos (n \tau - x \sin \tau) \,\mathrm{d}\tau. [/tex]
Sure. n=0, x=1.
 

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