Compute

∫π/20(sin8x)1/3(cosx)1/2dx.\ \int_0^{\pi/2}\dfrac{(\sin 8x )^{1/3}}{(\cos x)^{1/2}} dx .

using Gamma & Beta Function properties

This question make me suffer a lot.

I have used everything I am capable for and I failed

I evaluated this integral using Matlab , and the result was an imaginary number.

If anyone has any idea about this question please share it with me.

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There is indeed a big problem of definition because sin(8x)\sin(8x) is frequently negative on the interval of integration. Thus its power 1/31/3 will generate complex numbers. I doubt that this integral is amenable to a Beta integral…

– JeanMarie

2 days ago

so probably there is a mistake n the question @JeanMarie

– Feras Mohammed

2 days ago

@JeanMarie: I assume they use 3√−1=−1\sqrt[3]{-1}=-1.

– robjohn♦

2 days ago

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