A calculus problem by Saarthak Marathe

Calculus Level 5

$\large \displaystyle I= \int^{1}_{0} \dfrac { \tan^{-1}(\sqrt{2+x^2})}{(1+x^2)\sqrt{2+x^2}} \,dx$

Find the value of $\lfloor{1000I}\rfloor$ .

Notation: $\lfloor{\cdot}\rfloor$ denotes the floor function (greatest integer function).

The answer is 514.

1 solution

Mark Hennings
Oct 2, 2016

This is Ahmed's integral, equal to $\tfrac{5}{96}\pi^2$ . See my previous posting for a solution.

@Mark Hennings So what should I do to this problem??

Saarthak Marathe - 4 years, 8 months ago

Well, it is the same as the problem I posted a month ago...

Mark Hennings - 4 years, 8 months ago

It is curious that your problem didn't have so many solvers recently, and now there are a lot of these and rising quickly. Do you think computers works?It is an ironic , rhetorical question... This question was here (from you) a month ago, and there weren't so many solvers....

Guillermo Templado - 4 years, 8 months ago

Well, this version can be done numerically with WA. WA could not handle the exact version I set. That said, I still have more solvers. I guess it is quite a well-known integral.

Mark Hennings - 4 years, 8 months ago

It IS a quite famous integral, so he may have posted it independently.

Pratyush Pandey - 4 years, 8 months ago

I am sure he did. On the other hand, it is worth checking through the current listings to see if a problem has been posted previously before adding a new problem.

Mark Hennings - 4 years, 8 months ago

A calculus problem by Saarthak Marathe

The answer is 514.

1 solution

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