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GATE 2020 CE (CE1) – Question 49

Engineering Mathematics · Calculus: Integrals, partial and total derivatives, gradient, divergence, curl, line, surface and volume integrals · 2 marks · Numerical answer

C is the straight segment from (0,0,0) to (1,1,1). Evaluate $\int_C[(y+z)dx+(x+z)dy+(x+y)dz]$, expressed as an integer.

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Correct answer: 3 to 3

Explanation

Parameterize x = y = z = t, from 0 to 1. Each differential is dt and each coefficient is 2t. Integral is $\int_0^1 6t\,dt=\mathbf3$. Equivalently the field is the gradient of xy + xz + yz.