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Morewood
Lv 7
Morewood asked in Science & MathematicsMathematics · 7 years ago

Exact value of the Integral from 0 to 1 of Cos(Sin(pi*x))*Cosh(Cos(pi*x)) dx?

Update:

I get "1" using complex analysis, but shouldn't there be something more direct?

Update 2:

If I'm not going to get a serious answer, I should delete this. But that options seems to have disappeared!

Update 3:

I went to post my complex analysis solution, and found an error. So I really do not know the exact value... I really wish I could delete this!

2 Answers

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  • az_lender
    Lv 7
    4 years ago

    Since the indefinite integral of this expression can be written only with the help of the (complex) exponential integral Ei(x), it seems likely that your complex-analysis solution is the best approach. But don't be too contemptuous of numerical integration: at least it gives you an answer, to any desired degree of precision. In this case, the answer is certainly very close to 1 (just looking at a "fooplot" plot of the function), so your error may have had little or no effect. Good luck.

  • alex
    Lv 7
    7 years ago

    use a calculator ---> 1

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