$\displaystyle\int_{-1}^{1} \sin^5 x\cos^4 x\,dx$ equals

Question

Accepted Answer

B. $0$

1. Let $f(x)=\sin^5 x\cos^4 x$.
2. $f(-x)=\sin^5(-x)\cos^4(-x)=-\sin^5 x\cos^4 x=-f(x)$, so $f$ is odd.
3. By property $\mathbf{P_7}$(ii), the integral over $[-1,1]$ is $0$.
4. Option C would apply only if $f$ were even.
_Source: syllabus Mathematics Ch 7 "Integrals", p.344_

Answer

$1$

Answer

$2\displaystyle\int_0^1 \sin^5 x\cos^4 x\,dx$

Answer

$\dfrac{2}{9}$

$\displaystyle\int_{-1}^{1} \sin^5 x\cos^4 x\,dx$ equals

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