# GATE Questions & Answers of Integration

## What is the Weightage of Integration in GATE Exam?

Total 5 Questions have been asked from Integration topic of Calculus subject in previous GATE papers. Average marks 1.60.

The value of $\int_0^{\mathrm\pi/4}x\cos\left(x^2\right)dx$ correct to three decimal places (assuming that $\mathrm\pi=3.14$) is _________ .

If ${\int }_{0}^{2\mathrm{\pi }}\left|x\mathrm{sin}x\right|dx=k\mathrm{\pi },$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 $i=\sqrt{-1}$, what will be the evaluation of the definite integral $\int\limits_0^{\pi/2}\frac{\cos x+i\sin x}{\cos x-i\sin x}dx$ ?
$\int\limits_0^{\mathrm\pi/4}\left(1-\tan x\right)/\left(1+\tan x\right)\operatorname{d}x$