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Statement-1: $\int_{0}^{2 π} \cos^{2 m + 1} x d x = 0 (m > 0)$
Statement-2: $\int_{0}^{2 a} f (x) d x = 2 \int_{0}^{a} f (x) d x$

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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 A

∫02π cos2m+1⁡xdx=2∫0π cos2m+1⁡xdx=0( since cos⁡(π−x)=−cos⁡x)

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Statement-1: ∫02π cos2m+1⁡xdx=0(m>0)Statement-2:∫02a f(x)dx=2∫0a f(x)dx

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Statement-1: $\int_{0}^{2 π} \cos^{2 m + 1} x d x = 0 (m > 0)$
Statement-2: $\int_{0}^{2 a} f (x) d x = 2 \int_{0}^{a} f (x) d x$