Let a,b are constants.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]a=\int_{-∏}^∏ f(x)\,dx [/tex]

and

[tex]b=\int_{-∏}^∏ {g(x)f(x)}\,dx,[/tex]

Then by integration byparts, we have ,

b = [tex](\left.g(x)\int_{-∏}^∏ f(x)\,dx)\right|_{-∏}^∏-\int_{-∏}^∏g'(x)\int_{-∏}^∏ f(x)\,dx \,dx [/tex]

Is below step valid.

b = [tex]a(\left.g(x))\right|_{-∏}^∏-a\int_{-∏}^∏g'(x)\,dx [/tex]

I am not able to find it googling. Can an integral be replaced by a constant.

FYI : This came up when I am working on computing binomial coefficients with their trignometric form.

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# Can integral be replaced by constant

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