GATE | Sudo GATE 2020 Mock III (24 January 2019) | Question 19

Which of the following option is correct ?
(A) \int_{0}^{\infty} \mathrm{e}^{-x^2}\, dx = \frac{\sqrt \pi}{2}
(B) \int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx = \frac{\sqrt \pi}{2}
(C) Both (A) and (B)
(D) None of these.


Answer: (A)

Explanation:
[TEC] \int_{0}^{\infty} \mathrm{e}^{-x^2}\, dx = \frac{\sqrt \pi}{2}

\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}

So, option (A) is correct.

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