\(\displaystyle \int_{0}^{\frac{\pi}{2}}\frac{1}{2cos(x)+3}dx\)
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 ? \(\displaystyle \int_{0}^{k\cdot \pi}f=k\int_{0}^{\pi}f\)
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 ? \(\displaystyle \int_{0}^{k\cdot \pi}f=k\int_{0}^{\pi}f\)