GATE 2016 EE (EE2) – Question 19
Engineering Mathematics · Calculus: Vector identities, Directional derivatives, Line integral, Surface integral, Volume integral, Stokes's theorem, Gauss's theorem, Divergence theorem, Green's theorem · 1 mark · Multiple choice
Find $\int_C(2xy^2\,dx+2x^2y\,dy+dz)$ along a path from (0,0,0) to (1,1,1).
- 0
- 2
- 4
- 6
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Correct answer: (B) 2
Explanation
The integrand is the exact differential $d(x^2y^2+z)$. Consequently its integral depends only on the endpoints.
At (1,1,1) the potential is 1+1=2, while at the origin it is zero. Their difference is **2, B**, irrespective of the particular connecting path.
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