Evaluate: d x 1-2 x-x^2 - Vidyadip

MCQ

Evaluate: $\int \frac{d x}{\sqrt{1-2 x-x^2}}$

A
$\frac{1}{\sqrt{2}} \sin ^{-1}\left(\frac{1+x}{\sqrt{2}}\right)+C$
B
$\frac{1}{\sqrt{2}} \log (1+x)+C$
C
$\sin ^{-1}\left(\frac{1+x}{\sqrt{2}}\right)+C$
D
$\frac{1}{\sqrt{2}} \log \left(\frac{1+x}{\sqrt{2}}\right)+C$

✓

Answer

$
\begin{array}{l}
\text { (c) : Let } I=\int \frac{d x}{\sqrt{1-\left(x^2+2 x\right)}}=\int \frac{d x}{\sqrt{2-\left(x^2+2 x+1\right)}} \\
=\int \frac{d x}{\sqrt{2-(1+x)^2}}=\int \frac{d x}{\sqrt{(\sqrt{2})^2-(1+x)^2}}
\end{array}
$
Put $1+x=z \Rightarrow d x=d z$
$
\therefore I=\int \frac{d z}{\sqrt{(\sqrt{2})^2-z^2}}=\sin ^{-1} \frac{z}{\sqrt{2}}+C=\sin ^{-1}\left(\frac{1+x}{\sqrt{2}}\right)+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 "M.C.Q (1 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

In order to maximize the profit of the company, the optimal solution of which of the following equations is required?

P = x + y - 200
P = 5y - 2x
P = y - 80
P = 200 - x

Let $f : R \to R$ be a function such that $\left| {f\left( x \right)} \right| \leq {x^2}$ , for all $x \in R$ . Then, at $x\, = 0$, $f$ is

Find equation of line joining $(1,2)$ and $(3,6)$ using determinates

A set of vectors taken in a given order gives a closed polygon.Then the resultant of these vectors is:

scalar quantity
pseudo vector
unit vector
null vector

The lines $\frac{1-x}{3}=\frac{7 y-14}{2 p}=\frac{z-3}{2}$ and $\frac{7-7 x}{3 p}=\frac{y-5}{1}=\frac{6-z}{5}$ are at right angles then $p=$ _________.

The area enclosed by the curves y² = x and y = |x| is:

$\frac{2}{3}$
$1$
$\frac{1}{6}$
$\frac{1}{3}$

If the binary operation * on Z is defined by a * b = a² − b² + ab + 4, then value of (2 * 3) * 4 is:

233
33
55
−55

If a line makes an angle of $30^{\circ}$ with the positive direction of $x$-axis, $120^{\circ}$ with the positive direction of $y$-axis, then the angle which it makes with the positive direction of $z$-axis is :

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}+\vec{b}|^{2}=|\vec{a}|^{2}+2|\vec{b}|^{2}, \vec{a} \cdot \vec{b}=3 \quad$ and $\quad|\vec{a} \times \vec{b}|^{2}=75$.Then $|\vec{a}|^{2}$ is equal to $.......$

Let R be a relation on the set N given by R = {(a, b): a = b - 2, b > 6}. Then,

(2, 4) ∈ R
(3, 8) ∈ R
(6, 8) ∈ R
(8, 7) ∈ R