Evaluate _ -1 ^ 1 ^ 5 x ^ 4 x d x - Vidyadip

Question

Evaluate $\int_{-1}^{1} \sin ^{5} x \cos ^{4} x d x$

✓

Answer

b
Let $I=\int_{-1}^{1} \sin ^{5} x \cos ^{4} x d x .$ Let $f(x)=\sin ^{5} x \cos ^{4} x .$ Then

$f(-x)=\sin ^{5}(-x) \cos ^{4}(-x)=-\sin ^{5} x \cos ^{4} x=-f(x),$ i.e., $f$ is an odd function.

Therefore, by $P_{7}(\text { ii }), I=0$

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