Home › Previous year questions › GATE 2016 EE (EE2) › Question 41GATE 2016 EE (EE2) – Question 41 Engineering Mathematics · Calculus: Vector identities, Directional derivatives, Line integral, Surface integral, Volume integral, Stokes's theorem, Gauss's theorem, Divergence theorem, Green's theorem · 2 marks · Numerical answer
Find the line integral of $\mathbf F=5xz\hat{\mathbf i}+(3x^2+2y)\hat{\mathbf j}+x^2z\hat{\mathbf k}$ from (0,0,0) to (1,1,1), parametrized by $(t,t^2,t)$.
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Show answer and explanation Correct answer: 4.40 to 4.45
Explanation Use r(t)=(t,t²,t), 0≤t≤1, so r′=(1,2t,1). Along the curve F=(5t²,5t²,t³).
Their dot product is 5t²+10t³+t³=5t²+11t³. Integrating gives 5/3+11/4=53/12.
Therefore the line integral is **4.41667**, within 4.40–4.45.
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