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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, 9 months ago

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2 \times 3

2^{34}

a_{i-1}

\frac{2}{3}

\sqrt{2}

\sum_{i=1}^3

\sin \theta

\boxed{123}

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@Ishan Singh @Pi Han Goh

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

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

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

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`*italics*`

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italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

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Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

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TopNewest@Ishan Singh @Pi Han Goh

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

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

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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...Log in to reply

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