# GATE Questions & Answers of Line, Surface and Volume Integrals

## What is the Weightage of Line, Surface and Volume Integrals in GATE Exam?

Total 2 Questions have been asked from Line, Surface and Volume Integrals topic of Calculus subject in previous GATE papers. Average marks 1.50.

Given a vector field F= y2xax - yzay -x2az, the line integral evaluated along a segment on the x-axis from x =1 to x = 2 is

$\mathbf{F}\left(x,y\right)=\left({x}^{2}+xy\right){\stackrel{\mathbf{^}}{\mathbf{a}}}_{\mathbf{x}}+\left({y}^{2}+xy\right){\stackrel{\mathbf{^}}{\mathbf{a}}}_{y}$. It's line integral over the straight line from $\left(x,y\right)=\left(0,2\right)$ to $\left(x,y\right)=\left(2,0\right)$ evaluates to