First slide

Evaluation of definite integrals

Question

Statement-1: $\int_{- π / 3}^{π / 3} x^{10} \sin^{9} x d x = 0$
Statement-2: $f (x) = x^{2 n}$ is an even function and $g (x) = \sin^{2 m + 1} x$ 1x is an odd function, m and n are integers.

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

$x^{10} \sin^{9} x$ is an odd function so
$\int_{- a}^{a} x^{10} \sin^{9} x d x = 0$

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