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

$\int_{2}^{4} \frac{\log(x^2)}{\log(x^2) + \log(36 - 12x + x^2)} \, dx = $

$\int_0^{\pi / 2} \frac{2 \sin (x)+3 \cos (x)}{\sin (x)+\cos (x)} d x=$

For $0 \le x \le \frac{\pi}{2}$,the value of $\int_{0}^{\sin^{2}x} \sin^{-1}(\sqrt{t}) \, dt + \int_{0}^{\cos^{2}x} \cos^{-1}(\sqrt{t}) \, dt$ is equal to

$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \log \left(\frac{2019-x}{2019+x}\right) d x=$ . . . . . . .

Let $I = \int_{\pi / 4}^{\pi / 3} \frac{\sin x}{x} dx$. Then

Vedclass Test Series

Exam Paper Generator

Online Exam Module