Evaluate $\int_{0}^{a} \ cos^{a-1}x\ cos(a+1)x dx$ where $ a \in (0,\frac{\pi}{2}) $
I don't know the answer but it's one of these : $ cos^{a}a $ , $ sin^{a}a $ , $ acos^{a}a $ , $ 0 $ and another answer.
This one looks difficult to me, as a highschooler :s
To integrate this with parameter $a$ is not that easy, (though I am sure there is somebody out here who can do it), but it is a multiple choice question. If this is for High school, then I am sure they don't want you to integrate with $a$. So if you pick a suitable $a$, then you should be able to find an answer. So if you pick $a=1$, then we have $\int_{0}^{1} \ x\ cos(2x)dx$. This can be done with integration by parts. You may then verify that the anti derivative is $\frac{x \sin2x}2+\frac{cos2x}{4}$. With upper value $1$ and lower value $0$, we get $\frac{sin2}{2}+\frac{cos2}{4}-\frac{1}{4}$. Now when you plug in $a=1$ in the suggested answers, I greatly suspect that the correct answer is "and another answer", because the given answers don't work.