_ ^ 2x a^2 + b^2 ^2 x ;dx = - Vidyadip

MCQ

$\int_{}^{} {\frac{{\sin 2x}}{{{a^2} + {b^2}{{\sin }^2}x}}} \;dx = $

✓
$\frac{1}{{{b^2}}}\log ({a^2} + {b^2}{\sin ^2}x) + c$
B
$\frac{1}{b}\log ({a^2} + {b^2}{\sin ^2}x) + c$
C
$\log ({a^2} + {b^2}{\sin ^2}x) + c$
D
${b^2}\log ({a^2} + {b^2}{\sin ^2}x) + c$

✓

Answer

Correct option: A.

$\frac{1}{{{b^2}}}\log ({a^2} + {b^2}{\sin ^2}x) + c$

a
(a) Put ${a^2} + {b^2}{\sin ^2}x = t \Rightarrow {b^2}\sin 2x\,dx = dt,$ then
$\int_{}^{} {\frac{{\sin 2x}}{{{a^2} + {b^2}{{\sin }^2}x}}\,dx = \frac{1}{{{b^2}}}\int_{}^{} {\frac{{dt}}{t} = \frac{1}{{{b^2}}}\log t + c} } $
$ = \frac{1}{{{b^2}}}\log ({a^2} + {b^2}{\sin ^2}x) + 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

Which of the following functions is decreasing on $\left(0, \frac{\pi}{2}\right)$ ?

The volume $V$ and depth $ x $ of water in a vessel are connected by the relation $V = 5x - {{{x^2}} \over 6}$ and the volume of water is increasing at the rate of $5 \, c{m^3}/\sec $, when $x = 2\,cm$. The rate at which the depth of water is increasing, is

The order and the degree of differential equation $\frac{{{d^4}y}}{{d{x^4}}} - 4\frac{{{d^3}y}}{{d{x^3}}} + 8\frac{{{d^2}y}}{{d{x^2}}} - 8\frac{{dy}}{{dx}} + 4y = 0$ are respectively

If the co-ordinates of the points $A,B,C$ be $( - 1,\,3,\,2),\,\,(2,\,3,\,5)$ and $(3, 5,-2) $ respectively, then $\angle A = $ ..…… $^o$

If $f(x)$ is a quadratic in $x$ , then $\int\limits_0^1 {f(x) dx}$ is

$D$ is a $3 \times 3$ diagonal matrix. Which of the following statements is not true?

If $A=\left(\begin{array}{ll}{2} & {2} \\ {9} & {4}\end{array}\right)$ and $I=\left(\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\right),$ then $10 A^{-1}$ is equal to

If $A$ is a symmetric matrix, then matrix $M'AM$is

The area between the curve ${y^2} = 4ax,$ $x -$ axis and the ordinates $x = 0$ and $x = a$ is

If in a binomial distribution $\text{n}=4,\text{P(X}=0)=\frac{16}{81},$ then $\text{P(X}=4)$ equals:

$\frac{1}{16}$
$\frac{1}{81}$
$\frac{1}{27}$
$\frac{1}{8}$