GATE Mechanical 2022 Set 2 | Question: 4

Question

Given $\int_{-\infty }^{\infty } e^{-x^{2}} dx = \sqrt{\pi }.$

If $a$ and $b$ are positive integers, the value of $\int_{-\infty }^{\infty } e^{-a\left ( x+b \right )^{2}} dx$ is _______________.

• A. $\sqrt{\pi a}$

• A. $\sqrt{\frac{\pi }{a}}$

100. $b\sqrt{\pi a}$

500. $b\sqrt{\frac{\pi }{a}}$