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If $\int_{0}^{\infty} e^{- x^{2}} d x = \frac{\sqrt{π}}{2}$ then
Statement-1: $\int_{0}^{\infty} \frac{e^{- x}}{\sqrt{x}} d x = \sqrt{π}$
Statement-2: $lim_{x \to \infty} e^{- x^{2}} = 0$

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STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is False

STATEMENT-1 is False, STATEMENT-2 is True

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detailed solution

Correct option is B

Put x=t2∫0∞ e−xxdx=2∫0∞ e−t2ttdt=2∫0∞ e−t2dt

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If ∫0∞ e−x2dx=π2 thenStatement-1: ∫0∞ e−xxdx=πStatement-2: limx→∞ e−x2=0

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If $\int_{0}^{\infty} e^{- x^{2}} d x = \frac{\sqrt{π}}{2}$ then
Statement-1: $\int_{0}^{\infty} \frac{e^{- x}}{\sqrt{x}} d x = \sqrt{π}$
Statement-2: $lim_{x \to \infty} e^{- x^{2}} = 0$