Evaluate the following integrals: ^ -1 ( 2x 1- 2x )dx - Vidyadip

Question

Evaluate the following integrals:
$\int\cot^{-1}\Big(\frac{\sin2\text{x}}{1-\cos2\text{x}}\Big)\text{dx}$

✓

Answer

$\int\cot^{-1}\Big(\frac{\sin2\text{x}}{1-\cos2\text{x}}\Big)\text{dx}$
$=\int\cot^{-1}\Big(\frac{2\sin\text{x}\cos\text{x}}{2\sin^2\text{x}}\Big)\text{dx}$ $\big[\therefore\ \sin2\text{x}=2\sin\text{x}\cos\text{x} \text{ & }1-\cos2\text{x}=2\sin^2\text{x}\big]$
$=\int\cot^{-1}(\cot\text{x})\text{dx}$
$=\int\text{x dx}$
$=\frac{\text{x}^2}{2}+\text{C}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If -1 < x < 0, then write the value of $\sin^{-1}\Big(\frac{2\text{x}}{1+\text{cx}^2}\Big)+\cos^{-1}\Big(\frac{1-\text{x}^2}{1+\text{x}^2}\Big).$

If $x =\sin \theta, y =\tan \theta$, then find $\frac{ d y}{ d x}$

Let the p.m.f. of r.v. $X$ be $P ( x )={ }^4 C _x\left(\frac{5}{9}\right)^x\left(\frac{4}{9}\right)^{4-x}, x =0,1,2$, 3, 4. Find $E(X)$ and $\operatorname{Var}(X)$

$\int \frac{ e ^x \log \left(\sin e ^x\right)}{\tan e ^x} d x$

The vector $\overline{ a }$ is directed due north and $|\overline{ a }|=24$. The vector $\overline{ b }$ is directed due west and $|\overline{ b }|=7$. Find $|\overline{ a }+\overline{ b }|$.

Let $R=\left\{\left(a, a^3\right)\right.$ : $a$ is a prime number less than 5$\}$ be a relation. Find the range of $R$.

A random variable X has the following probability distribution:

Values of X:	-2	-1	0	1	2	3
P(X)	0.1	k	0.2	2k	0.3	k

Find the value of k.

Find the acute angle between the lines $x = y, z = 0$ and $x = 0, z = 0$

Write the identity relation on set A = {a, b, c}.

Solve: $1+\frac{d y}{d x}=\operatorname{cosec}(x+y)$; put $x+y=u$.