GATE Questions & Answers of Integration

What is the Weightage of Integration in GATE Exam?

Total 4 Questions have been asked from Integration topic of Calculus subject in previous GATE papers. Average marks 1.75.

If 02πxsinxdx=kπ,then the value of k is equal to ______ .

The value of the integral given below is

$\int\limits_0^\mathrm\pi x^2\cos xdx$

Given i=-1, what will be the evaluation of the definite integral $\int\limits_0^{\pi/2}\frac{\cos x+i\sin x}{\cos x-i\sin x}dx$ ?

$\int\limits_0^{\mathrm\pi/4}\left(1-\tan x\right)/\left(1+\tan x\right)\operatorname{d}x$

evaluates to