# GATE Questions & Answers of Multiple Integrals

## What is the Weightage of Multiple Integrals in GATE Exam?

Total 2 Questions have been asked from Multiple Integrals topic of Calculus subject in previous GATE papers. Average marks 2.00.

To evaluate the double integral $\int\limits_0^8\left(\int\limits_\frac y2^{\left(\frac y2\right)+1}\left(\frac{2x-y}2\right)dx\right)dy$,we make the substitution $u=\left(\frac{2x-y}{2}\right)$ and $v=\frac{y}{2}$ The integral will reduce to

f(x,y) is a continuous function defined over (x,y)$\in$ [0,1] × [0,1]. Given the two constraints, x > y2 and y > x2, the volume under f(x,y) is