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

MCQ

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

✓
$\frac{1}{{2(b - a)}}\log (a{\cos ^2}x + b{\sin ^2}x) + c$
B
$\frac{1}{{b - a}}\log (a{\cos ^2}x + b{\sin ^2}x) + c$
C
$\frac{1}{2}\log (a{\cos ^2}x + b{\sin ^2}x) + c$
D
None of these

✓

Answer

Correct option: A.

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

a
(a) Put $a{\cos ^2}x + b{\sin ^2}x = t$$ \Rightarrow 2(b - a)\sin x\cos x = dt,$
then $\int_{}^{} {\frac{{\sin x\cos x\,dx}}{{a{{\cos }^2}x + b{{\sin }^2}x}} = \frac{1}{{2(b - a)}}\int_{}^{} {\frac{1}{t}\,dt} } $
$ = \frac{1}{{2(b - a)}}\log (a{\cos ^2}x + b{\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 STD 12 - 7.1 inderfinite integral→STD 12 - 7.1 inderfinite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $\alpha \,(a \times b) + \beta \,(b \times c) + \gamma \,(c \times a) = 0$ and at least one of the numbers $\alpha ,\,\,\beta $ and $\gamma $ is non-zero, then the vectors $a, b$ and $c$ are

If $\frac{d y}{d x}=\frac{2^{x} y+2^{y} \cdot 2^{x}}{2^{x}+2^{x+y} \log _{e} 2}, y(0)=0$, then for $y=1$ the value of $x$ lies in the interval:

If the function $f : R \rightarrow A$ given by $\text{f(x)}=\frac{\text{x}^2}{\text{x}^2+1}$ is a surjection, then $ A =$

The value of $\sum \limits_{n=0}^{1947} \frac{1}{2^n+\sqrt{2^{1994}}}$ is equal to

Let $n \ge 2$ be a natural number and $0 < \theta < \frac{\pi }{2}$. Then $\int {\frac{{{{\left( {{{\sin }^n}\,\theta - \sin \,\theta } \right)}^{\frac{1}{n}}}\,\cos \,\theta }}{{{{\sin }^{n + 1}}\,\theta }}} d\theta $ is equal to

The value of $\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)+2 \cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$ :

The number of distinct real roots of $\left|\begin{array}{lll}\sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x\end{array}\right|=0$ in the interval $-\frac{\pi}{4} \leq x \leq \frac{\pi}{4}$ is

The function $f(x)=x+\frac{4}{x}$ has

If $B$ is a non$-$singular matrix and $A$ is a square matrix, then det $(B^{-1}AB)$ is equal to:

Let $f : R \rightarrow R$ be defined as $\text{f(x)}=\begin{cases}2\text{x},&\text{if x}>3\\\text{x}^2,&\text{if }1<\text{x}\leq3\\3\text{x},&\text{if x}\leq1\end{cases}.$ Then, find $f(-1) + f(2) + f(4):$