dx ( a^2 + x^2 ) ^ 3/2 is equal to - Vidyadip

MCQ

$\int {\frac{{dx}}{{{{({a^2} + {x^2})}^{3/2}}}}} $ is equal to

A
$\frac{x}{{{{\left( {{a^2} + {x^2}} \right)}^{1/2}}}}$
✓
$\frac{x}{{{a^2}{{\left( {{a^2} + {x^2}} \right)}^{1/2}}}}$
C
$\frac{1}{{{a^2}{{\left( {{a^2} + {x^2}} \right)}^{1/2}}}}$
D
None of these

✓

Answer

Correct option: B.

$\frac{x}{{{a^2}{{\left( {{a^2} + {x^2}} \right)}^{1/2}}}}$

b
(b) $I = \int{dx\over{(a^2 + x^2)^3/2}}$
Put $x = a\tan \theta \,\, \Rightarrow dx = a{\sec ^2}\theta \,d\theta $
$\therefore \,I = \int {\frac{{a{{\sec }^2}\theta }}{{{{({a^2} + {a^2}{{\tan }^2}\theta )}^{3/2}}}}d\theta } = \int {\frac{{a{{\sec }^2}\theta }}{{{a^3}{{({{\sec }^2}\theta )}^{3/2}}}}d\theta } $
==> $I = \frac{1}{{{a^2}}}\int {\frac{{d\theta }}{{\sec \theta }}} $ $ = \frac{1}{{{a^2}}}\int {\cos \theta \,d\theta = \frac{1}{{{a^2}}}\sin \theta + c} $
==> $I = \frac{x}{{{a^2}{{({x^2} + {a^2})}^{1/2}}}} + c$.

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 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $N$ be the set of natural numbers and a relation $R$ on $N$ be defined by $R=\left\{(x, y) \in N \times N: x^{3}-3 x^{2} y-x y^{2}+3 y^{3}=0\right\} .$ Then the relation $R$ is:

If $\int_0^1 {x\log \left( {1 + \frac{x}{2}} \right)} \,dx = a + b\log \frac{2}{3},$ then

If $f(x) = \left\{ \begin{array}{l}\frac{{1 - \cos x}}{x},\,x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,k,\,x = 0\end{array} \right.$ is continuous at $x = 0$ then $k = $

$\int_{}^{} {\sqrt {1 + {x^2}} \;dx = } $

Area between the curve $\text{y}=\cos^2\text{x},$ x-axis and ordinates x = 0 and x = p in the interval (0, p) is:

$2\pi3$
$2\pi$
$\pi$
$\frac{\pi}{2}$

Let $\vec a\, = \,\hat i\, + \,\hat j\, + \,\sqrt 2 \hat k,\,\,\vec b\, = \,{b_1}\hat i\, + \,{b_2}\hat j\, + \sqrt 2 \hat k$ and $\vec c\, = \,5\hat i\, + \,\hat j + \sqrt 2 \hat k$ be three vectors such that the projection vector of $\vec b$ on $\vec a$ is $\vec a$. If $\vec a\, + \vec b$ is perpendicular to $\vec c$ , then $\left| {\vec b} \right|$ is equal to

Let $S=(0,1) \cup(1,2) \cup(3,4)$ and $T=\{0,1,2,3\}$. Then which of the following statements is(are) true ?

($A$) There are infinitely many functions from $S$ to $T$

($B$) There are infinitely many strictly increasing functions from $\mathrm{S}$ to $\mathrm{T}$

($C$) The number of continuous functions from $\mathrm{S}$ to $\mathrm{T}$ is at most $120$

($D$) Every continuous function from $\mathrm{S}$ to $\mathrm{T}$ is differentiable

$\int\limits_0^\pi {{e^{{{\cos }^4}x}}} . \cos^5(2n + 1)x \,dx, (n \in I)$ is equal to

Which of the following is the integrating factor of $x d y / d x-y=x^4-3 x$ ?

If A and B are two independent events with $\text{P(A)}=\frac{3}{5}$ and $\text{P(B)}=\frac{4}{9},$ then $\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$ equals,

$\frac{4}{15}$
$\frac{8}{45}$
$\frac{1}{3}$
$\frac{2}{9}$