What is the technique that should be used to evaluate \int_{0}^{2\pi} (\sin (k\sin \theta))^2 d\t

Zugdichte2r

Zugdichte2r

Answered question

2022-01-27

What is the technique that should be used to evaluate 02π(sin(ksinθ))2dθ?

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Answer & Explanation

Brenton Pennington

Brenton Pennington

Beginner2022-01-28Added 15 answers

Hint:
02π(sin(ksinθ))2dθ=02π12(1cos(2ksinθ))dθ
where
0πcos(xsint)dt=πJ0(x)
and J0 is Bessel function of order 0.

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