The value of int_{-3}^3 sin ^7 x cos ^{16} x | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $f(x) = \sin^7 x \cos^{16} x$. We check if the function is even or odd by evaluating $f(-x)$. $f(-x) = \sin^7(-x) \cos^{16}(-x)$. Since $\sin(

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(C) Let $f(x) = \sin^7 x \cos^{16} x$. We check if the function is even or odd by evaluating $f(-x)$. $f(-x) = \sin^7(-x) \cos^{16}(-x)$. Since $\sin(-x) = -\sin x$ and $\cos(-x) = \cos x$,we have: $f(-x) = (-\sin x)^7 (\cos x)^{16} = -\sin^7 x \cos^{16} x = -f(x)$. Since $f(-x) = -f(x)$,the function $f(x)$ is an odd function. According to the property of definite integrals,if $f(x)$ is an odd function,then $\int_{-a}^a f(x) \,dx = 0$. Therefore,$\int_{-3}^3 \sin^7 x \cos^{16} x \,dx = 0$.

The value of $\int_{-3}^3 \sin ^7 x \cos ^{16} x \,dx$ is

Similar Questions

If $I_{n}=\int_0^{\frac{\pi}{4}} \tan ^n x \, dx$,then $I_{13}+I_{11}=$

$\int_0^{2 \pi} \frac{x \cos x}{1+\cos x} d x=$

Let $f:(0,2) \rightarrow R$ be defined as $f(x) = \log_{2}\left(1+\tan\left(\frac{\pi x}{4}\right)\right)$. Then,$\lim_{n \rightarrow \infty} \frac{2}{n}\left(f\left(\frac{1}{n}\right)+f\left(\frac{2}{n}\right)+\ldots+f(1)\right)$ is equal to

$\int_{-1}^{1} x \tan^{-1} x \, dx$ equals

Evaluate the integral: $\int_0^\pi \frac{x}{\sin x}(3 \cos^2 x + 2 \sin x + \sin^3 x - 3) dx$

Vedclass Test Series

Exam Paper Generator

Online Exam Module