[itex]\int^{\pi}_{0} f(x) dx[/itex] where ,(adsbygoogle = window.adsbygoogle || []).push({});

f(x) = sin x if [itex]0 \leq x < \frac{\pi}{2}[/itex]

and f(x) = cos(x) if [itex]\frac{\pi}{2} \leq x \leq \pi[/itex]

The problem is that the version I am using of Fundamental theorem is if f is continuous on some closed interval , I wrote the integral as

[itex]\int^{\pi / 2}_{0} f(x) dx + \int^{\pi}_{\pi /2} f(x) dx[/itex]

but I have in the first integral f still is not continuous on [itex][0,\pi/2][/itex]

I tried to open some references and reached another version for the theorem there f is integrable on f , and g' =f , but I couldn't do any thing

Thanks

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# A problem with evaluating an integral

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