Home › Previous year questions › GATE 2019 AE › Question 24GATE 2019 AE – Question 24 Engineering Mathematics · Calculus: Limits, continuity, differentiability, chain rule, maxima and minima, integration · 1 mark · Numerical answer
For $f(x)=\tfrac12(x+|x|)$, evaluate $\int_{-1}^{1}f(x)\,dx$.
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Show answer and explanation Correct answer: 0.5 to 0.5
Explanation For x<0, |x|=−x and f=0. For x≥0, f=x. Split the integral at zero: the negative part vanishes and the positive part is $\int_0^1x\,dx=1/2$. Answer 0.5.
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