List of top Mathematics Questions on Definite Integral asked in WBJEE

If \(I_n=\int_{0}^{\frac{\pi}{2}}cos^nxcos\,nxdx\), then \(I_1,I_2,I_3\).....are in

The average ordinate of y=sin x over [0,\(\pi\)] is

\(\int_{0}^{2\pi}\theta sin^6\theta cos\theta\,d\theta\) is equal to

If $\int \, f(x) \, \sin \, x \, \cos \, x \, dx = \frac{1}{2(b^2 - a^2)} \log f(x) + c$, where c is the constant of integration , then f(x) =

The value of the integral $\int\limits_{0}^{\pi / 2} \frac{1}{1+(\tan x)^{101}} d x$ is equal to

The value of $ \displaystyle\lim_{n\to\infty} \left[\frac{n}{n^{2}+1^{2}}+\frac{n}{n^{2}+2^{2}}+\ldots+\frac{1}{n^{2}+2n}\right] $ is