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GATE 2021 CE (CE2) – Question 28

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

Evaluate $\int_{-1}^1xe^{|x|}\,dx$ to one decimal.

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Correct answer: 0 to 0

Explanation

The factor $e^{|x|}$ is even while x is odd, making their product odd. Integrating an odd continuous function over symmetric limits gives zero because the positive and negative halves cancel. **Answer: 0.0.**