Mumbai university > Electronics and telecommunication engineering, Electronics engineering > Sem 3 > Applied mathematics 3

Marks : 04

Years : MAY 2016

By Stoke's Theorem $\int\limits_c \bar F. d\vec r=\int\int\limits_s(\triangledown\times \bar F).\hat N \space ds $

$\triangledown\times \bar F= \begin{vmatrix}i&j&\bar k\\ d/dx & d/dy & d/dz \\ x^2 & -xy & 0 \\ \end{vmatrix} =\bar k(-y-0) = -y\bar k \\ \hat N =\bar k, ds=dxdy\\ \int\limits_c\bar F.d\vec r= \int\limits_{x=0}^{a}\int\limits_{y=0}^a (-y) dxdy =\int\limits_{x=0}^a (-dx) [y^2/2]^a_0 \space[a^2/2] =\dfrac {-a^3}2$