I am having trouble with the definition of indefinite orthogonal group. On Wikipedia, it says it is the Lie group of all linear transformations of an n-dimensional real vector space that leave invariant a nondegenerate, symmetric bilinear form of signature (p, q), where n = p + q. However, this d...
Evaluating $\int_0^{\pi/2} \log(a^2\cos^2 x+b^2\sin^2 x) dx$ using the concept of differentiation under integral sign.
My Attempt:
Given
$$\int_0^{\pi/2} \log (a^2 \cos^2 x+b^2 \sin^2 x) dx$$
Here, $a$ and $b$ are parameters. Considering $b$ as a constant
$$F(a)=\int_0^{\pi/2} \log(a^2 \cos...
Evaluating $\int_0^{\pi/2} \log(a^2\cos^2 x+b^2\sin^2 x) dx$ using the concept of differentiation under integral sign.
My Attempt:
Given
$$\int_0^{\pi/2} \log (a^2 \cos^2 x+b^2 \sin^2 x) dx$$
Here, $a$ and $b$ are parameters. Considering $b$ as a constant
$$F(a)=\int_0^{\pi/2} \log(a^2 \cos...
