Exams › GATE › Engineering Mathematics
The value of the line integral ∫_C (2xy² dx + 2x²y dy + dz) along a path joining the origin (0, 0, 0) and the point (1, 1, 1) is
- 0
- 2
- 4
- 6
Correct answer: 2
Solution
The line integral evaluates the work done along the specified path, and in this case, the contributions from the terms in the integral simplify to yield a total value of 2 when calculated from the origin to the point (1, 1, 1).
Related GATE Engineering Mathematics questions
- A vector field p and a scalar field r are given by
p = (2x² - 3xy + z²) î + (2y² - 3yz + x²) ĵ + (2z² - 3xz + x²) k̂
r = 6x² + 4y² - z² - 9xyz - 2xy + 3xz - yz
Consider the statements P and Q.
P: Curl of the gradient of the scalar field r is a null vector.
Q: Divergence of curl of the vector field p is zero.
Which one of the following options is CORRECT?
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- Three vectors p, q and r are given as p = î + ĵ + k̂, q = î + 2ĵ + 3k̂, r = 2î + 3ĵ + 4k̂. Which of the following is/are CORRECT?
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