The Little Monster Integral

Calculus Level 5

The following integral involving inverse trigonometric and trigonometric functions has a gee-whiz closed-form

∫ 0 π 2 a r c c o t 1 + sin ⁡ θ sin ⁡ θ d θ = π α β {\large\int_0^{\Large\frac{\pi}{2}}} {\rm{arccot}}\sqrt{\frac{1+\sin\theta}{\sin\theta}}\,\,d\theta={\large\frac{\pi^{\alpha}}{\beta}}

Find the value of α + β \large\alpha+\beta .


The answer is 14.

Anastasiya Romanova by Anastasiya Romanova , 20, Russia

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1 solution

Tunk-Fey Ariawan
Oct 24, 2014

Hint: See Coxeter's Integral and Ahmed's Integral

2 Helpful 0 Interesting 0 Brilliant 0 Confused

You may use Feynman's way or double integration method to evaluate both integrals and of course your OP too. Nice problem anyway, thanks for sharing. :)

Tunk-Fey Ariawan - 6 years, 7 months ago

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You're welcome and +1. I know this integral is still one family with Coxeter's Integral, but I don't know it's a family of Ahmed's Integral. I solve it using Feynman's trick and here is a similar problem from Math SE that I recently solved. Have a look please... (❛‿❛✿̶̥̥)

Anastasiya Romanova - 6 years, 7 months ago

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