GATE EE 2016 Set 2 — Question 19
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Engineering Mathematics → Vector Calculus → Line, Surface & Volume Integrals
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Question
The value of the line integral along a path joining the origin and the point is
Correct answer
(B) 2
Solution
To evaluate the line integral , we first check if the vector field is conservative. The curl of is:Since the curl is zero, the field is conservative. We find the potential function such that .
Integrating with respect to gives .
Differentiating with respect to gives , so is a function of only.
Differentiating with respect to gives , so .
Thus, .
The line integral is .
Integrating with respect to gives .
Differentiating with respect to gives , so is a function of only.
Differentiating with respect to gives , so .
Thus, .
The line integral is .
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