Find: x ^ -1 x 1 - x^ 2 dx. - Vidyadip

Question

Find: $\int \frac{x \sin^{-1} x}{\sqrt{1 - x^{2}}} \text{d}x.$

✓

Answer

$\text{I} = \int \frac{\text{x} \sin^{-1} \text{x}}{\sqrt{1 - \text{x}^{2}}} \text{ dx}$
$\text{put} \sin^{-1} \text{x = t} \Rightarrow \frac{\text{dx}}{\sqrt{1 - \text{x}^{2}}} = \text{dt}$
$= \int \text{t.} \sin \text{t dt}$
$ = \text{ - t} \cos \text{t} + \sin \text{t + c}$
$= -\sqrt{1 - \text{x}^{2}} \sin^{-1} \text{x + x + c}$

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 "4 Marks" from INTEGRALS→INTEGRALS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Show that $\text{A}=\begin{bmatrix} 5 & 3 \\-1 & -2 \end{bmatrix}$ satisfies the equation x² - 3x - 7 = 0. Thus, find A^-1.

Evaluate the following intregals:
$\int\frac{\text{x}}{(\text{x}^2-\text{a}^2)(\text{x}^2-\text{b}^2)}\ \text{dx}$

If $\text{A}=\begin{bmatrix}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{bmatrix},$ find A^-1 and show that $\text{A}^{-1}=\frac{1}{2}(\text{A}^2-3\text{I}).$

Evaluate the following integrals as limit of sum:
$\int\limits^3_1(3\text{x}-2)\text{dx}$

Solve the following differential equation:
$2\text{xy dx}+(\text{x}^2+2\text{y}^2)\text{dy}=0$

Evaluate the following integrals:
$\int\limits^{\pi}_0\frac{\text{x}}{1+\cos\alpha\sin\text{x}}\text{ dx},0<\alpha<\pi$

If AB = BA for any two sqaure matrices, prove by mathematical induction that (AB)ⁿ = AⁿBⁿ.

Write the set of values of 'a' for which $\text{f}(\text{x})=\log_\text{a}\text{x}$ is decreasing in its domain.

Maximize $Z=4 x+y$ subject to constraints $x+y$ $\leq 50,3 x+y \leq 90, x \geq 0, y \geq 0$ by using graphical method.

Express the following matrix as the sum of a symmetric and a skew symmetric matrix, and verify your result:
$\begin{pmatrix}3&-2&-4\\3&-2&-5\\-1&1&2\end{pmatrix}$