GATE ME 2016 Set 2 — Question 36
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Engineering Mathematics → Vector Calculus → Conservative Vector Fields
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Question
A scalar potential has the following gradient: . Consider the integral on the curve .The curve is parameterized as follows: and .The value of the integral is ________
Correct answer
725.9 to 726.1
Solution
The given gradient is . This is a conservative vector field because it is the gradient of a scalar potential function .According to the Fundamental Theorem for Line Integrals, the integral of a gradient field over a path depends only on the endpoints of the path:The curve is parameterized by for as:
1.Find the start point ():
2.Find the end point ():
3.Calculate the integral value:
Value .Thus, the value of the integral is 726.Continue learning with Success Tracker
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