_0^ 2 , , dx 1 , , + , , a^2 ^2 x has the value : - Vidyadip

MCQ

$\int\limits_0^{\frac{\pi }{2}} {\,\,\frac{{dx}}{{1\,\, + \,\,{a^2}{{\sin }^2}x}}} $ has the value :

✓
$\frac{\pi }{{2\,\sqrt {1\, + \,{a^2}} }}$
B
$\frac{\pi }{{\sqrt {1\, + \,{a^2}} }}$
C
$\frac{{2\,\pi }}{{\sqrt {1\, + \,{a^2}} }}$
D
none

✓

Answer

Correct option: A.

$\frac{\pi }{{2\,\sqrt {1\, + \,{a^2}} }}$

a
$I = \int\limits_0^{\frac{\pi }{2}} {\,\,\frac{{{{\sec }^2}x\,dx}}{{1 + {{\tan }^2}x + {a^2}{{\tan }^2}x}}} $ $= \int\limits_0^{\frac{\pi }{2}} {\,\,\frac{{{{\sec }^2}x\,dx}}{{(1 + {a^2}){{\tan }^2}x + 1}}} $

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 STD 12 - 7.2 definite integral→STD 12 - 7.2 definite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Area included between the two curves ${y^2} = 4ax$ and ${x^2} = 4ay,$ is

The area bounded by the curve $y = x^2 - 1$ and the straight line $x + y = 3$ is:

The area of the region bounded by the curves $y =| x – 2 |, x = 1, x = 3$ and the $x-$axis is:

$\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{1}^{99}}+{{2}^{99}}+{{3}^{99}}+......{{n}^{99}}}{{{n}^{100}}}=$

If $\int {\frac{{dx}}{{{{\left( {{x^2} - 2x + 10} \right)}^2}}} = A\left( {{{\tan }^{ - 1}}\left( {\frac{{x - 1}}{3}} \right) + \frac{{f\left( x \right)}}{{{x^2} - 2x + 10}}} \right)} + C$ Where $C$ is a constant of integration, then

Let $A$ and $B$ be two events. If $\text{P(A)}=0.2,\text{P(B)}=0.4,\text{P}(\text{A}\cup\text{B})=0.6$ then $P(A|B)$ is equal to

The equation of the curve passing through $(3 , 4) \,\&$ satisfying the differential equation,
$y {\left( {\frac{{dy}}{{dx}}} \right)^2} + (x - y) \frac{{dy}}{{dx}} - x = 0 $ can be

Let $f(x) = x^3 -6x^2 +15x + 3.$ Then :

Let $R$ be a relation on the set $N$ of natural numbers defined by $\text{nRm}$ if $n$ divides $m.$ Then$, R$ is:

A non-zero vector $a$ is parallel to the line of intersection of the plane determined by the vectors $i,\,\,i + j$ and the plane determined by the vectors $i - j,\,\,i + k.$ The angle between $a$ and the vector $i - 2j + 2k$ is