If ∫ e^{-x^2} dx = √π/2 ; x ∈ [0, ∞], then ∫ e^{ax^2} dx(a > 0) ; x ∈ [0, ∞] is equal to

Question

If \(\int\limits_0^\infty e^{-x^2}dx = \frac{\sqrt \pi}2\), then \(\int \limits_0^\infty e^{-ax^2} dx(a>0)\) is equal to

a. \(\frac{\sqrt\pi}2\)

b. \(\frac{\sqrt\pi}{2a}\)

c. \(\frac{2\sqrt\pi}a\)

d. \(\frac{\sqrt\pi}{2\sqrt a}\)

Answer 1

Correct option is d. \(\frac{\sqrt\pi}{2\sqrt a}\)