GATE Electronics and Communications (EC) 2019 Solved Paper

Question : 62 of 65

Marks: +1, -0

Consider the line integral

∫↙{c}(x d y-y d x)

the integral being taken in a counterclockwise direction over the closed curve C that forms the boundary of the region R shown in figure below. The region R is the area enclosed by the union of a 2 × 3 rectangle and a semi-circle of radius 1. The line integral evaluates to

$16+2 π$
$8+π$
$12+π$
$6+2π$

Validate

Solution:

By greens theorem

∫ x d y-y d x=0 \;\;d x d y

∫(x d y-y d x)=0

2

= area of the region

\;\; =[2 × 3+\;{π(1)^{2}}/{2}]

[6+\;{π}/{2}]

∴ ∫( {xdy}- {ydx})=12+π

Go to Question:

Prev Question

Next Question