GATE EC 2017 Set 1 — Question 28
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Engineering Mathematics → Vector Calculus → Line, Surface & Volume Integrals
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Question
Let where are real, and let be the straight line segment from point to point . The value of is ________.
Correct answer
-11.1
Solution
The given line integral is where .
First, we check if the vector field is conservative by calculating its curl:Since the curl is zero, the field is conservative. There exists a potential function such that .
Integrating the components:
The value of the line integral for a conservative field is independent of the path and is given by the difference in the potential function at the endpoints:
Given and :
.
First, we check if the vector field is conservative by calculating its curl:Since the curl is zero, the field is conservative. There exists a potential function such that .
Integrating the components:
1.
2.
3.
Combining these, we get the potential function .The value of the line integral for a conservative field is independent of the path and is given by the difference in the potential function at the endpoints:
Given and :
.
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