GATE 2021 CE (CE1) – Question 29

Engineering Mathematics · Calculus: Integrals, partial and total derivatives, gradient, divergence, curl, line, surface and volume integrals · 1 mark · Numerical answer

Evaluate $\iiint_V8xyz\,dV$ for $V=[2,3]\times[1,2]\times[0,1]$ (integer).

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Correct answer: 15 to 15

Explanation

The rectangular domain lets the integral separate as $8(\int_2^3x\,dx)(\int_1^2y\,dy)(\int_0^1z\,dz)$. The three factors are 5/2, 3/2 and 1/2. Their product with 8 is **15**.