GATE CE 2020 Set 1 — Question 49
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Engineering Mathematics → Vector Calculus → Line Integrals
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Question
If represents a line segment between and in Cartesian coordinate system, the value (expressed as integer) of the line integralis ___________.
Correct answer
3 to 3
Solution
The given line integral is of the form , where .Step 1: Check if the vector field is conservative.
A vector field is conservative if its curl is zero:Since the curl is zero, the field is conservative, meaning the line integral is path-independent.Step 2: Find the potential function such that .
A vector field is conservative if its curl is zero:Since the curl is zero, the field is conservative, meaning the line integral is path-independent.Step 2: Find the potential function such that .
1.
2.
3.
Thus, the potential function is .Step 3: Evaluate the line integral using the Fundamental Theorem of Line Integrals.Continue learning with Success Tracker
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