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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, 7 months ago

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- 1 year, 7 months ago

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

- 1 year, 7 months ago

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

- 1 year, 7 months ago

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.

- 1 year, 7 months ago

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...

- 1 year, 7 months ago

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

- 1 year, 7 months ago