If _0^ k d x 2+8 x^2 = 16 , then k = - Vidyadip

MCQ

If $\int_0^{ k } \frac{ d x}{2+8 x^2}=\frac{\pi}{16}$, then $k =$

A
1
✓
$\frac{1}{2}$
C
$\frac{1}{4}$
D
$\frac{1}{8}$

✓

Answer

Correct option: B.

$\frac{1}{2}$

(B)
$\int_0^{ k } \frac{ d x}{2+8 x^2}=\frac{\pi}{16}$
$\Rightarrow \frac{1}{2} \int_0^k \frac{1}{1^2+(2 x)^2} d x=\frac{\pi}{16}$
$\Rightarrow \frac{1}{2}\left[\frac{\tan ^{-1}(2 x)}{2}\right]_0^{ k }=\frac{\pi}{16}$
$\Rightarrow \frac{1}{4}\left(\tan ^{-1} 2 k \right)=\frac{\pi}{16}$
$\Rightarrow \tan ^{-1} 2 k =\frac{\pi}{4} \Rightarrow k =\frac{1}{2}$

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 Definite Integration→Definite Integration — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

$\int_3^8 \frac{2-3 x}{x \sqrt{(1+x)}} d x$ is equal to

The determinant $\begin{vmatrix}\text{b}^2-\text{ab}&\text{b}-\text{c}&\text{bc}-\text{ac}\\\text{ab}-\text{a}^2&\text{a}-\text{b}&\text{b}^2-\text{ab}\\\text{bc}-\text{ac}&\text{c}-\text{a}&\text{ab}-\text{a}^2\end{vmatrix}$ equals:

A bakerman sells 5 types of cakes. Profit due to sale of each type of cake is respectively ₹ 3 , ₹ 2.5, ₹ 2 , ₹ 1.5 and ₹ 1 . The demands for these cakes are 10%, 5%, 20%, 50% and 15% respectively. Then, the expected profit per cake is

$\int_{-2}^2|x| d x$ is equal to

If $\text{y}=\sin^{-1}\Big(\frac{1-\text{x}^2}{1+\text{x}^2}\Big),$ then $\frac{\text{dy}}{\text{dx}}=$

If $\int \tan ^3 x \cdot \sec ^3 x \cdot d x=\left(\frac{1}{m}\right) \sec ^m x-\left(\frac{1}{n}\right) \sec ^n x+c$, then $(m, n)=$

If $\hat{i} ,\hat{j},\hat{k} $ are the unit vectors and mutually perpendicular, then [$\hat{i} ,\hat{k},\hat{j} $] is equal to

Angle between two planes $\bar{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=6$ and $\bar{r} \cdot(\hat{i}+\hat{j}+2 \hat{k})=5$ is

A fair coin is tossed a fixed number of times. If the probability of getting seven heads is equal to that of getting nine heads, the probability of getting two heads is:

If $\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}$, then the value of $x^{100}+y^{100}+z^{100}-\frac{9}{x^{101}+y^{101}+z^{101}}$ is equal to