Evaluate $\int\limits_{-1}^{1} \sin^5 x \cos^4 x \, dx$
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0
Let $I = \int\limits_{-1}^{1} \sin^5 x \cos^4 x \, dx$. Let $f(x) = \sin^5 x \cos^4 x$. Then
$f(-x) = \sin^5 (-x) \cos^4 (-x) = -\sin^5 x \cos^4 x = -f(x), \text{ i.e., } f \text{ is an odd function.}$
Therefore, $I = 0$