int (3 csc^2 x + 2 sin 3x) , dx = | vedclass

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

Question

(B) We need to evaluate the integral $\int (3 \csc^2 x + 2 \sin 3x) \, dx$. Using the linearity property of integration,we can write this as $\int 3 \

Vedclass · Accepted Answer

$- (3 \cot x + \frac{2}{3} \cos 3x) + c$

Vedclass · Answer

(B) We need to evaluate the integral $\int (3 \csc^2 x + 2 \sin 3x) \, dx$. Using the linearity property of integration,we can write this as $\int 3 \csc^2 x \, dx + \int 2 \sin 3x \, dx$. The integral of $\csc^2 x$ is $-\cot x$ and the integral of $\sin(ax)$ is $-\frac{1}{a} \cos(ax)$. Thus,$\int 3 \csc^2 x \, dx = -3 \cot x$ and $\int 2 \sin 3x \, dx = 2 \left( -\frac{1}{3} \cos 3x \right) = -\frac{2}{3} \cos 3x$. Combining these,we get $-3 \cot x - \frac{2}{3} \cos 3x + c$. Factoring out the negative sign,we get $-(3 \cot x + \frac{2}{3} \cos 3x) + c$.

$\int (3 \csc^2 x + 2 \sin 3x) \, dx = $

Similar Questions

$\int \frac{\sin x + \csc x}{\tan x} \, dx = $

For $x \in \left(\frac{3 \pi}{4}, \pi\right)$, evaluate the integral $\int(\sqrt{1+\sin 2 x}+\sqrt{1-\sin 2 x}) \, dx$.

$\int \tan^4 x \, dx = $

If $\int \frac{dx}{\sqrt{2ax - x^2}} = f(g(x)) + c$, where $c$ is the constant of integration, then $f(x)$ and $g(x)$ are respectively equal to:

Let $x \neq \frac{-3}{5}, \frac{2}{5}$. If $f\left(\frac{2x+1}{5x+3}\right) = x+2$, then $\int f(x) dx =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module