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Impossible Integral

Is it possible to find \(\int\sin(\sin\theta)\mbox{ d}\theta\)?

Note by Kenny Lau
3 years, 5 months ago

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I think ... the question is ill posed. Indefinite integrals don't have a "value". Sometimes you can't have a closed formula for some functions, yet for specific limit values you cand find out the exact integral value

Omm Yucatan - 3 years, 5 months ago

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Thanks for your reminder. I've updated the question.

Kenny Lau - 3 years, 5 months ago

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Assume \sin\theta =t We have \cos\theta dø = dt,by difrentiat it \cos\theta =\sqrt{t^{2}-1} So new function is \frac{ \sin\theta }{\sqrt{t^{2}-1} Solve this function by part ,may be we a solution

Prabhat Sharma - 3 years, 5 months ago

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\[t=\sin\theta\] \[\frac{\mbox{d}t}{\mbox{d}\theta}=\cos\theta\] \[\mbox{d}\theta=\frac{\mbox{d}t}{\sqrt{1-t^2}}\] \[\begin{array}{rcl} I&=&\int\sin(\sin\theta)\mbox{ d}\theta\\ &=&\int\frac{\sin t\mbox{ d}t}{\sqrt{1-t^2}} \end{array}\]

Kenny Lau - 3 years, 5 months ago

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