GATE 2018 CE (CE2) – Question 47

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

For $\mathbf F(\mathbf r)=x^2\hat i+y^2\hat j$, evaluate $\int_C\mathbf F\cdot d\mathbf r$ along the straight segment from (0,0) to (1,1), to two decimals.

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Correct answer: 0.60 to 0.70

Explanation

Parameterize the segment as $\mathbf r(t)=(t,t)$, $0\le t\le1$. Then $\mathbf F=(t^2,t^2)$ and $d\mathbf r=(1,1)dt$. Thus $\int_0^1 2t^2\,dt=2/3=0.67$ to two decimals.