^ _01 1+ dx equals: - Vidyadip

MCQ

$\int\limits^{\pi}_0\frac{1}{1+\sin\text{x}}\text{ dx}$ equals:

A
$0$
B
$\frac{1}{2}$
✓
$2$
D
$\frac{3}{2}$

✓

Answer

Correct option: C.

$2$

$\int\limits^{\pi}_0\frac{1}{1+\sin\text{x}}\text{ dx}$
$=\int\limits^\pi_0\frac{1}{1+\sin\text{x}}\times\frac{1-\sin\text{x}}{1-\sin\text{x}}\text{dx}$
$= \int\limits^\pi_0\frac{1-\sin\text{x}}{1-\sin^2\text{x}}\text{dx}$
$= \int\limits^\pi_0\frac{1-\sin\text{x}}{\cos^2\text{x}}\text{dx}$
$=\int\limits^\pi_0(\sec^2\text{x}-\sec\text{x}\tan\text{x})\text{dx}$
$=\big[\tan\text{x}-\sec\text{x}\big]^\pi_0$
$=0+1-0+1$
$=2$

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

Similar questions

The edge of a cube is decreasing at the rate of $0.6 cm / sec$ then the rate at which its volume is decreasing when the edge of the cube is $2 cm$, is

Which of the following statement is true

If $\overline{ a }=2 \overline{ p }+3 \overline{ q }-\overline{ r }, \overline{ b }=\overline{ p }-2 \overline{ q }+2 \overline{ r }$ and $\bar{c}=-2 \bar{p}+\bar{q}-2 \bar{r}$ and $\bar{R}=3 \bar{p}-\bar{q}+2 \bar{i}$, where $\bar{p}, \bar{q}, \bar{r}$ are non-coplanar vectors, then $\overline{ R }$ in terms of $\overline{ a }, \overline{ b }, \overline{ c }$ is

The equation $3 x^2+2 h x y+y^2=0$ represents a pair of straight lines passing through the origin. Then two lines are

Area bounded between two latus-rectum of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 ; a>b$ is ___________ .
(where, c is eccentricity of the ellipse)

The number of solutions of the equation $\tan^{-1}2\text{x}+\tan^{-1}3\text{x}=\frac{\pi}{4}$ is:

$\int_0^\pi x f(\sin x) d x$ is equal to

If $\int \frac{d x}{4 x^2-1}=A \log \left(\frac{2 x-1}{2 x+1}\right)+c,$ then $A= ........ $

If $3\sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)-4\cos^{-1}\Big(\frac{1-\text{x}^2}{1+\text{x}^2}\Big)+2\tan^{-1}\Big(\frac{2\text{x}}{1-\text{x}^2}\Big)=\frac{\pi}{3}$ is equal to:

If $\sin ^{-1}\left(\frac{2 a}{1+a^2}\right)+\sin ^{-1}\left(\frac{2 b}{1+b^2}\right)=2 \tan ^{-1} x$, then $x=$