Project ForgeEngineering Mathematics
Linear Algebra
GATE 2015
Medium
A vector u=−2yî+2xĵ. Evaluate the line integral I=∮_C u·dr, where C is the closed loop (1,1)→(3,1)→(3,2)→(1,2)→(1,1). The value of I is
8
Explanation
By Green's theorem: I=∬(∂Q/∂x−∂P/∂y)dA=∬(2−(−2))dA=4×Area=4×(2×1)=8.
Source: GATE CH 2015 (2015)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.