Choose the correct answer in Exercises : ^2x- ^2x ^2x ^2x dx is e… - Vidyadip

MCQ

Choose the correct answer in Exercises : $\int\frac{\sin^2\text{x}-\cos^2\text{x}}{\sin^2\text{x}\cos^2\text{x}}\text{ dx}$ is equal to

✓
$\tan\text{x}+\cot\text{x}+\text{C}$
B
$\tan\text{x}+\text{cosec x}+\text{C}$
C
$-\tan\text{x}+\cot\text{x}+\text{C}$
D
$\tan\text{x}+\sec\text{x}+\text{C}$

✓

Answer

Correct option: A.

$\tan\text{x}+\cot\text{x}+\text{C}$

$\int\frac{\sin^2\text{x}-\cos^2\text{x}}{\sin^2\text{x}\cos^2\text{x}}\text{ dx}$
$=\int\bigg(\frac{\sin^2\text{x}}{\sin^2\text{x}\cos^2\text{x}}-\frac{\cos^2\text{x}}{\sin^2\text{x}\cos^2\text{x}}\bigg)\text{dx}$
$=\int(\sec^2\text{x}-\text{cosec}^2\text{x})\text{ dx}$
$=\tan\text{x}+\cot\text{x}+\text{C}$
Hence, the correct answer is $A$.

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

More "M.C.Q (1 Marks)" from INTEGRALS→INTEGRALS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If X follows a binomial distribution with parameter $\text{n}=8$ and $\text{p}=\frac{1}{2},$ then $\text{P(|X}-4|\leq2)$ equals:

If $a = i - j,b = i + j,\,\,\,c = i + 3j + 5k$ and $n$ is a unit vector such that $b.n = 0,a.n = 0$ then the value of $|c\;.\;n|$ is equal to

The solution of the equation $\left[ {\begin{array}{*{20}{c}}1&0&1\\{ - 1}&1&0\\0&{ - 1}&1\end{array}} \right]\,\left[ \begin{array}{l}x\\y\\z\end{array} \right] = \left[ \begin{array}{l}1\\1\\2\end{array} \right]$ is $(x,y,z)$=

The area $($in $sq.$ units$)$ bounded by the curves $\text{y}=\sqrt{\text{x}},2\text{y}-\text{x}+3=0$ and $x-$axis lying in the first quadrant is:

The value of $x$ for which $\left(x-x^2\right)$ is maximum, is

The value of the integral $\int \limits_{-\pi / 2}^{\pi / 2} \frac{d x}{\left(1+e^{x}\right)\left(\sin ^{6} x+\cos ^{6} x\right)}$ is equal to

If$f(x) = \left\{ \begin{array}{l}{e^{1/x}},\;{\rm{when}}\;x \ne 0\\0,\;\;\;\;\;{\rm{when}}\;x = 0\end{array} \right.$, then

$Q^{+}$ denote the set of all positive rational numbers. If the binary operation $\text{a }\odot$ on $Q^{+}$ is defined as: $\text{a }\odot=\frac{\text{ab}}{2}$, then the inverse of $3$ is:

Let $f: R \rightarrow R$ be defined as $f(x)=3 x .$ Choose the correct answer.

If $\begin{bmatrix} 1 & -\tan\theta \\ \tan\theta & 1 \end{bmatrix}\begin{bmatrix} 1 & \tan\theta \\ -\tan\theta & 1 \end{bmatrix}-1=\begin{bmatrix} \text{a} & -\text{b} \\ \text{b} & \text{a} \end{bmatrix},$ then: