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Let $I = \int_{- \infty}^{\infty} \frac{d x}{1 + x^{2}}$
Statement-1: $I = π$
Statement-2: The integrand is even and $\lim_{b \to \infty} F (b)$
$= π, F (b) = \int_{0}^{b} \frac{d x}{1 + x^{2}}$

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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 forSTATEMENT-1

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detailed solution

Correct option is C

The integrand is even, so∫-∞∞dx1+x2=2∫0∞dx1+x2∫0∞dx1+x2=limb→∞∫0bdx1+x2=limb→∞tan-1b-0=π2

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Let I=∫-∞∞dx1+x2Statement-1:I =π Statement-2: The integrand is even and limb→∞F(b)=π,F(b)=∫0bdx1+x2

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free study material

Let $I = \int_{- \infty}^{\infty} \frac{d x}{1 + x^{2}}$
Statement-1: $I = π$
Statement-2: The integrand is even and $\lim_{b \to \infty} F (b)$
$= π, F (b) = \int_{0}^{b} \frac{d x}{1 + x^{2}}$