_ 1 / 4 ^ 1 / 2 d x x-x^2 = - Vidyadip

MCQ

$\int_{1 / 4}^{1 / 2} \frac{d x}{\sqrt{x-x^2}}=$

A
$\pi$
B
$\frac{\pi}{2}$
C
$\frac{\pi}{3}$
✓
$\frac{\pi}{6}$

✓

Answer

Correct option: D.

$\frac{\pi}{6}$

(D)
$\int_{1 / 4}^{1 / 2} \frac{d x}{\sqrt{x-x^2}}=\int_{1 / 4}^{1 / 2} \frac{d x}{\sqrt{\left(\frac{1}{2}\right)^2-\left(x-\frac{1}{2}\right)^2}}$
$=\left[\sin ^{-1}\left(\frac{x-\frac{1}{2}}{\frac{1}{2}}\right)\right]_{\frac{1}{4}}^{\frac{1}{2}}$
$=\left[\sin ^{-1}(2 x-1)\right]_{1 / 4}^{1 / 2}=\frac{\pi}{6}$

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

If $\text{A}=\begin{bmatrix}1&\text{a}\\0&1\end{bmatrix},$ then $A^n ($where $n \in N)$ equals:

Let $f(x)=\int \frac{x^2-3 x+2}{x^4+1} d x$, then function decreases in the interval

If the angle between the planes $\bar{r} \cdot(x \hat{i}+\hat{j}-\hat{k})=4$ and $\bar{r} \cdot(\hat{i}+x \hat{j}+\hat{k})=-1$ is $\frac{\pi}{3}$, then the value of $x$ is

If the volume of the parallelopiped with coterminous edges $-p \hat{j}+5 \hat{k}, \hat{i}-\hat{j}+q \hat{k}$ and $3 \hat{i}-5 \hat{j}$ is 8 , then

The direction cosines of Y -axis are

The points $A (1,0,1), B (-1,2,3)$ and $C(0,1,2)$ are

The p.m.f. of a r.v. X is

X = x	1	2	3	....	n
P(X = x)	$\frac{1}{n}$	$\frac{1}{n}$	$\frac{1}{n}$	....	$\frac{1}{n}$

Then the standard deviation of X is

If planes $x-c y-b z=0, c x-y+a z=0$ and $b x+a y-z=0$ pass through straight line, then $a^2+b^2+c^2=$

The centroid of the triangle formed by the lines $x+3 y=10$ and $6 x^2+x y-y^2=0$ is

The negation of 'If it is sunday then it is a holiday' is