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Let $I = \int_{0}^{π} \frac{\cos x}{\sqrt{1 - \sin^{2} x}} d x$
Statement-1: $I = π$
Statement-2: The integrand can be expressed as $X_{[0, π / 2]} X_{[π / 2, π]}; X_{A}$ being the characteristic function of A.

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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

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 D

cosx1-sin2x=cos|cosx|=1x∈[0,π/2]-1,x∈(π/2,π)∫0πcosx1-sin2x=∫0π/2dx-∫π/2πdx=0

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Let I=∫0πcosx1-sin2xdx Statement-1: I=πStatement-2: The integrand can be expressed as X[0,π/2]X[π/2,π];XA being the characteristic function of A.

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free study material

Let $I = \int_{0}^{π} \frac{\cos x}{\sqrt{1 - \sin^{2} x}} d x$
Statement-1: $I = π$
Statement-2: The integrand can be expressed as $X_{[0, π / 2]} X_{[π / 2, π]}; X_{A}$ being the characteristic function of A.