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(x + b)^2}dx is _________.

GATE Mechanical Engineering (ME) 2022 Shift 2 Solved Paper

Question : 14 of 65

Marks: +1, -0

Given

∫ _{−∞}^{∞}e^{−x^{2}}dx = {√{π }}

If a and b are positive integers, the value of

∫ _{−∞}^{∞}e^{−a(x + b)^2}dx

is _________.

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