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

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

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