Download App

7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int {\frac{{{x^2}}}{{\left( {{x^2} + 1} \right)\left( {{x^2} + 4} \right)}}\,} dx$ is equal to
  • A
    $ - {\tan ^{ - 1}}x + \frac{1}{3}{\tan ^{ - 1}}\frac{x}{2} + C$
  • ✓
    $- \frac{1}{3}{\tan ^{ - 1}}x + \frac{2}{3}{\tan ^{ - 1}}\frac{x}{2} + C$
  • C
    ${\tan ^{ - 1}}x + \frac{2}{3}{\tan ^{ - 1}}\frac{x}{2} + C$
  • D
    $\frac{1}{3}{\tan ^{ - 1}}x - \frac{2}{3}{\tan ^{ - 1}}\frac{x}{2} + C$
✓

Answer

Correct option: B.
$- \frac{1}{3}{\tan ^{ - 1}}x + \frac{2}{3}{\tan ^{ - 1}}\frac{x}{2} + C$
b
consider $\frac{x^{2}}{\left(x^{2}+1\right)\left(x^{2}+4\right)}$ and put $x^{2}=y$

Then $\frac{x^{2}}{\left(x^{2}+1\right)\left(x^{2}+4\right)}=\frac{y}{(y+1)(y+4)}$

Write $\frac{y}{(y+1)(y+4)}=\frac{A}{(y+1)}+\frac{B}{(y+4)}$

so that $y=A(y+4)+B(y+1)$

$\therefore \quad A=-\frac{1}{3}  $ and $ B=\frac{4}{3}$

$\therefore \mathrm{I}=\int \frac{-\frac{1}{3}}{\left(\mathrm{x}^{2}+1\right)} \mathrm{dx}+\int \frac{4 / 3}{\left(\mathrm{x}^{2}+4\right)} \mathrm{dx}$

$=-\frac{1}{3} \tan ^{-1} \mathrm{x}+\frac{2}{3} \tan ^{-1}\left(\frac{\mathrm{x}}{2}\right)+\mathrm{C}$

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

$\int_{\pi /4}^{\pi /2} {\cos \theta \,{\rm{cose}}{{\rm{c}}^{\rm{2}}}\theta \,d\theta = } $
→
If $a, b $ and $c $ are unit vectors, then $|a - b{|^2} + |b - c{|^2} + |c - a{|^2}$ does not exceed
→
$a, b, c$ are three non-zero, non-coplanar vectors and $p, q, r$ are three other vectors such that $p = \frac{{b \times c}}{{a\,.\,b \times c}}$,$q = \frac{{c \times a}}{{a\,.\,b \times c}}$, $r = \frac{{a \times b}}{{a\,.\,b \times c}}$. Then $[p\,q\,r]$ equals
→
If $\cos\alpha,\cos\beta,\cos\gamma$ are the direction cosines of a vector $\vec{\text{a}}$ then $\cos2\alpha+\cos2\beta+\cos2\gamma$ is equal to:
  1. 2
  2. 3
  3. -1
  4. 0
→
The value of $\frac{e^{-\frac{\pi}{4}}+\int \limits_0^{\frac{\pi}{4}} e^{-x} \tan ^{50} x d x}{\int \limits_0^{\frac{\pi}{4}} e^{-x}\left(\tan ^{49} x+\tan ^{51} x\right) d x}$ is
→
If the position vectors of three points $A,B$ and $C$ are respectively $ i + j + k, 2i + 3j -4k$  and  $7i + 4j + 9k,$  then the unit vector to the plane containing the triangle $ABC$ is
→
The domain of the function $\cos ^{-1}(2 x-1)$ is
→
The minimum number of times one has to toss a fair coin so that the probability; of observing at least one head is at least $90\%$ is
→
The plane $2\text{x}-(1-\lambda)\text{y}+3\lambda\text{z}=0$ passes through the intersection of the planes:
→
Given $A$ and $C$ are involutary matrices and $B$ is a non-singular matrix, then $(AB^{-1}C)^{-1}$ is equal to -
→