GATE EC 2023 Set 1 — Question 37
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Engineering Mathematics → Vector Calculus → Line, Surface & Volume Integrals
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Question
The value of the line integral along the straight line joining the points and is
Correct answer
(B) 24
Solution
To evaluate the line integral , we first check if the vector field is conservative.
Calculating the curl of :Since the curl is zero, the field is conservative. We find the potential function such that :
The value of the integral is :
Integral .
Calculating the curl of :Since the curl is zero, the field is conservative. We find the potential function such that :
1.
2.
3.
Combining these, we get .The value of the integral is :
Integral .
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