2x- 2 - dx is equal to: - Vidyadip

MCQ

$\int\frac{\cos2\text{x}-\cos2\theta}{\cos\text{x}-\cos\theta}\text{ dx}$ is equal to:

✓
$2(\sin\text{x}+\text{x}\cos\theta)+\text{C}$
B
$2(\sin\text{x}-\text{x}\cos\theta)+\text{C}$
C
$2(\sin\text{x}+2\text{x}\cos\theta)+\text{C}$
D
$2(\sin\text{x}-2\text{x}\cos\theta)+\text{C}$

✓

Answer

Correct option: A.

$2(\sin\text{x}+\text{x}\cos\theta)+\text{C}$

$\text{I}=\int\frac{\cos2\text{x}-\cos2\theta}{\cos\text{x}-\cos\theta}\text{ dx}$
$\text{I}=\int\frac{2\cos^2\text{x}-1-(2\cos^2\theta-1)}{\cos\text{x}-\cos\theta}\text{ dx}$
$\text{I}=\int\frac{2(\cos^2\text{x}-\cos^2\theta)}{\cos\text{x}-\cos\theta}\text{ dx}$
$\text{I}=2\int(\cos\text{x}+\cos\theta)\text{dx}$
$\text{I}=2(\sin\text{x}+\text{x}\cos\theta)+\text{C}$

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 "MCQ" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

$\int_0^\pi|\cos x| d x=$

P.d.f. of a c.r.v. X is f(x) = 6x(1 – x), for 0 ≤ x ≤ 1 and = 0, otherwise (elsewhere) If P(X < a) = P(X > a), then a =

Every conditional statement is equivalent to

If $\int_{\log 2}^a \frac{ e ^x}{\sqrt{ e ^x-1}} d x=2$, then $a =$

The equation $x-y$ $=4$ and $x^2+4 x y+y^2=0$ represent the sides of a/an

Let $\bar{a}=\hat{i} \hat{j}, \bar{b}=\hat{j} \hat{k}_{\text {, }} \bar{c}=\hat{k} \hat{i}$. If $\bar{d}$ is a unit vector such that $\bar{a} \cdot \bar{d}=0=\left[\begin{array}{lll}\bar{b} & \bar{c} & \bar{d}\end{array}\right]$, then $\bar{d}$ equals.

If $U =\left[\begin{array}{ll}\frac{1}{\sqrt{2}} & \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}}\end{array}\right]$, then $U ^{-1}$ is

The value of $\int_0^{2 x} \cos ^{99} x d x$ is

If $A = \{1, 2, 3\}, B = \{1, 4, 6, 9\}$ and $R$ is a relation from $A$ to $B$ defined by $'x$ is greater than $y'$. The range of $R$ is:

If ABCD is a parallelogram and the position vectors of $A, B, C$ are $\hat{i}+3 \hat{j}+5 \hat{k}, \hat{i}+\hat{j}+\hat{k}$ and $7\hat{i}+7 \hat{j}+7 \hat{k}$, then the position vector of D will be