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Q.

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

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a

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

b

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

c

STATEMENT-1 is True, STATEMENT-2 is False

d

STATEMENT-1 is False, STATEMENT-2 is True

answer is A.

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Detailed Solution

∫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