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Does this have a closed form?

Does the following expression have a closed form? \[\int_0^{\frac{\pi}{2}} x^{\sin x + \cos x} \, dx\]

Note by Deeparaj Bhat
1 year, 5 months ago

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@Ishan Singh @Pi Han Goh

Deeparaj Bhat - 1 year, 5 months ago

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I seriously doubt it's possible. Why do you think a closed form exists in the first place?

Pi Han Goh - 1 year, 5 months ago

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Because it was asked in an examination :P (the exact way is given in this question)

Deeparaj Bhat - 1 year, 5 months ago

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@Deeparaj Bhat The point of that question is to find the integer part of the numerical value of that integral, not the exact form of the integral.

Pi Han Goh - 1 year, 5 months ago

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@Pi Han Goh I know. But many times, they give stuff whose closed form can be found using out of syllabus stuff but we're expected to get bounds via elementary methods. So, I was curious...

Deeparaj Bhat - 1 year, 5 months ago

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@Deeparaj Bhat Don't worry about it. There are infinitely many integrals that don't have a closed form.

Pi Han Goh - 1 year, 5 months ago

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