Download App

STD 12 - 7.2 definite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.2 definite integral4 Marks
MCQ
Given that $\int_0^\infty {\frac{{{x^2}\,dx}}{{({x^2} + {a^2})({x^2} + {b^2})({x^2} + {c^2})}} = \frac{\pi }{{2(a + b)(b + c)(c + a)}}} ,$ then the value of $\int_0^\infty {\frac{{{x^2}dx}}{{({x^2} + 4)({x^2} + 9)}}} $ is
  • ✓
    $\frac{\pi }{{60}}$
  • B
    $\frac{\pi }{{20}}$
  • C
    $\frac{\pi }{{40}}$
  • D
    $\frac{\pi }{{80}}$
✓

Answer

Correct option: A.
$\frac{\pi }{{60}}$
a
(a) Put $a = 2, b = 3$ and $c = 0$  in the given integral and you get the value of required integral as given in option $ (a).$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $a , b , c$ be three non-zero real numbers such that the equation $\sqrt{3} a \cos x +2 b \sin$ $x=c, x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$, has two distinct real roots a and $\beta$ with $a+\beta=\frac{\pi}{3}$. Then, the value of $\frac{ b }{ a }$ is. . . . . . .
→
If $X$ and $Y$ are two independent binomial variates, satisfying $B\left( {10,\frac{1}{2}} \right)$ and $B\left( {8,\frac{1}{2}} \right)$ respectively, then probability $P\left( {X + Y = 2} \right)$ is
→
An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number $2$ times is equal to the probability of getting an even number $3$ times, then the probability of getting an odd number for odd number of times is
→
Let $a_n$ denote the number of all n-digit positive integers formed by the digits $0,1$ or both such that no consecutive digits in them are $0$ . Let $b_n=$ the number of such $n$-digit integers ending with digit $1$ and $c_n=$ the number of such $n$-digit integers ending with digit $0$ .

$1.$ Which of the following is correct?

$(A)$ $a_{17}=a_{16}+a_{15}$ $(B)$ $c_{17} \neq c_{16}+c_{15}$

$(C)$ $b_{17} \neq b_{16}+c_{16}$ $(D)$ $a_{17}=c_{17}+b_{16}$

$2.$ The value of $b_6$ is

$(A)$ $7$ $(B)$ $8$ $(C)$ $9$ $(D)$ $11$

Give the answer question $1$ and $2.$

→
Let $f :[0,1] \rightarrow R$ be a twice differentiable function in $(0,1)$ such that $f (0)=3$ and $f (1)=5$. If the line $y=2 x+3$ intersects the graph of $f$ at only two distinct points in $(0,1)$, then the least number of points $x \in(0,1)$, at which $f ^{\prime \prime}( x )=0$, is$......$
→
In a series of $2n$ observation, half of them are equal to $'a'$  and remaining half observations are equal to $' -a'$. If the standard deviation of this observations is $2$ then $\left| a \right|$ equals
→
Let $f(\theta ) = \sin \theta (\sin \theta + \sin 3\theta )$, then $f(\theta )$
→
If $f(x) = \frac{{x - 3}}{{x + 1}}$, then $f[f\{ f(x)\} ]$ equals
→
The value of  $\operatorname{Lim}_{n \rightarrow \infty} \frac{1+2-3+4+5-6+\ldots+(3 n-2)+(3 n-1)-3 n}{\sqrt{2 n^4+4 n+3-} \sqrt{n^4+5 n+4}}$ is :
→
If $a$ is non zero vector of modulus   $ a $ and $m$  is a non-zero scalar, then $ma$ is a unit vector if
→