why the result is changing?

Vali

Junior Member
Joined
Feb 27, 2018
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\(\displaystyle \int_{0}^{\frac{\pi}{2}}\frac{1}{2cos(x)+3}dx\)
I solved this and I get the answer \(\displaystyle \frac{2}{\sqrt{5}}arctan\frac{1}{\sqrt{5}}\)
Why if I take 1/2 out the result is changing ? By solving \(\displaystyle \frac{1}{2}\int_{0}^{\pi}\frac{1}{2cos(x)+3}dx\) I get another answer.
When I'm allowed to use this ? \(\displaystyle \int_{0}^{k\cdot \pi}f=k\int_{0}^{\pi}f\)
 
That would only be true for specific functions, one of which I can think of would be a constant function.

[MATH]\int_0^{ka} b\,dx=b(ka-0)=abk[/MATH]
[MATH]k\int_0^a b\,dx=kb(a-0)=abk[/MATH]
 
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