_0^ / 2 x x 1+ ^4 x d x= - Vidyadip

MCQ

$\int_0^{\pi / 2} \frac{\sin x \cos x}{1+\sin ^4 x} d x=$

A
$\frac{\pi}{2}$
B
$\frac{\pi}{4}$
C
$\frac{\pi}{6}$
✓
$\frac{\pi}{8}$

✓

Answer

Correct option: D.

$\frac{\pi}{8}$

(D)
Put $\sin ^2 x= t \Rightarrow 2 \sin x \cos x d x= dt$
When $x=0, t =0$ and when $x=\frac{\pi}{2}, t =1$
$\therefore \int_0^{\pi / 2} \frac{\sin x \cos x}{1+\sin ^4 x} d x=\frac{1}{2} \int_0^1 \frac{1}{1+ t ^2} dt =\frac{1}{2}\left[\tan ^{-1} t \right]_0^1=\frac{\pi}{8}$

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

$2 \int \frac{\cos ^2 x-\sin ^2 x}{\cos ^2 x+\sin ^2 x} \cdot d x=$

The area of the figure bounded by the parabolas $x=-2 y^2$ and $x=1-3 y^2$ is

$\int_0^{2 \pi} e ^{\frac{x}{2}} \cdot \sin \left(\frac{x}{2}+\frac{\pi}{4}\right) d x=$

If the events $A$ and $B$ are independent, then $\text{P}(\text{A}\cap\text{B})$ is equal to,

If the random variable $X$ has the following distribution:

$X:$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X):$	$a$	$3a$	$5a$	$7a$	$9a$	$11a$	$13a$	$15a$	$17a$

then the value of $a$ is:

The angle between the line $\bar{r}=(2 \hat{i}+3 \hat{j}+\hat{k})+\lambda(\hat{i}+2 \hat{j}-\hat{k})$ and the plane $\bar{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=4$ is

Which of the following transformation reduce the differential quation into the form
$\frac{\text{du}}{\text{dx}}+\text{P}(\text{x})\text{u}=\text{Q}(\text{x})$ into the from $\frac{\text{dz}}{\text{dx}}+\frac{\text{z}}{\text{x}}\log\text{z}=\frac{\text{z}}{\text{x}^{2}}(\log\text{z})^{2}$

The differential equation of the ellipse $\frac{\text{x}^{2}}{\text{a}^{2}}+\frac{\text{y}^{2}}{\text{b}^{2}}=\text{C}$ is:

If three points $A , B$ and C have co-ordinates (1, x, 3), (3,4,7) and (y,-2,-5) respectively. They are collinear, then $x, y=$

$\int \tan \left(\sin ^{-1} x\right) \cdot d x=$