GATE 2018 CS – Question 26
The value of $\displaystyle\int_0^{\pi/4}x\cos(x^2)\,dx$ correct to three decimal places (assuming that $\pi=3.14$) is ________.
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Correct answer: 0.28 to 0.30
Explanation
Let $u=x^2$: the integral is $\frac12\sin\left(\frac{\pi^2}{16}\right)=\frac12\sin(0.6162)=\frac12(0.5779)=0.289$.