If 8x+1 2x- 2x dx=a 8x+C, then a = - Vidyadip

MCQ

If $\int\frac{\cos8\text{x}+1}{\tan2\text{x}-\cot2\text{x}}\text{ dx}=\text{a}\cos8\text{x}+\text{C},$ then $a =$

A
$-\frac{1}{16}$
B
$\frac{1}{8}$
✓
$\frac{1}{16}$
D
$-\frac{1}{8}$

✓

Answer

Correct option: C.

$\frac{1}{16}$

$\int\frac{\cos8\text{x}+1}{\tan2\text{x}-\cot2\text{x}}\text{ dx}$
$=\int\frac{2\cos^24\text{x}}{\frac{\sin2\text{x}}{\cos2\text{x}}-\frac{\cos2\text{x}}{\sin2\text{x}}}\text{ dx}$
$=\int\frac{2\cos^24\text{x}}{\sin^22\text{x}-\cos^22\text{x}}\times\sin2\text{x}\cos2\text{x dx}$
$=\int-\frac{\cos^24\text{x}\sin4\text{x}}{\cos4\text{x}}\text{ dx}$
$=\frac{-1}{2}\int\sin8\text{x dx}$
$=\frac{\cos8\text{x}}{16}+\text{C}$
$\text{a}=\frac{1}{16}$

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

Solution of differential equation $\frac{{dy}}{{dx}} = 2xy$ is

Let $P ( x )= x ^{2}+ bx + c$ be a quadratic polynomial with real coefficients such that $\int_{0}^{1} P ( x ) dx =1$ and $P ( x )$ leaves remainder $5$ when it is divided by $(x-2)$. Then the value of $9(b+c)$ is equal to:

If $g:[ - 2,\,2] \to R$ where $g(x) = $ ${x^3} + \tan x + \left[ {\frac{{{x^2} + 1}}{P}} \right]$ is a odd function then the value of parametric $P$ is

If matrix $A=\left[a_{i j}\right]_{2 \times 2}$, where $a_{i j}=\left\{\begin{array}{l}1, \text { if } i \neq j \\ 0, \text { if } i=j\end{array}\right.$ then $A^2$ is equal to

$\text{I}=\int\frac{(\text{x+a})^3}{\text{x}^3}\text{dx}$ is equal to:

$\int_{a}^{b}\text{x}^2\text{dx}=$

If $\vec a,\vec b,\vec c$ are non- zero and non-coplanar vectors such that $\left( {\vec a + \lambda \vec b} \right).\left[ {\left( {\vec b + 3\vec c} \right) \times \left( {\vec c - 4\vec a} \right)} \right] = 0$ , then $\lambda $ is equal to

For $x \in R$ , $f\left( x \right) = \left| {\log 2 - \sin x} \right|$ and $g\left( x \right) = f\left( {f\left( x \right)} \right)$ then .. .

Two dice are rolled one after the other. The probability that the number on the first is smaller than the number on the second is

$\frac{1}{2}{\cos ^{ - 1}}\left( {\frac{{1 - x}}{{1 + x}}} \right) = $