First slide

Evaluation of definite integrals

Question

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

Easy

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

Solution

$\begin{array}{l} \int_{0}^{2 π} \cos^{2 m + 1} x d x = 2 \int_{0}^{π} \cos^{2 m + 1} x d x \\ = 0 (since \cos (π - x) = - \cos x) \end{array}$

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