_ - / 2 ^ / 2 x 1+ ^2 x e^ - ^2 x d x is equal to - Vidyadip

MCQ

$\int_{-\pi / 2}^{\pi / 2} \frac{\sin x}{1+\cos ^2 x} e^{-\cos ^2 x} d x$ is equal to

A
$2 e^{-1}$
B
1
✓
$0$
D
-1

✓

Answer

Correct option: C.

$0$

(C)
Let $f (x)=\frac{\sin x}{1+\cos ^2 x} e ^{-\cos ^2 x}$
$\begin{array}{ll}\therefore & f (-x)=-\frac{\sin x}{1+\cos ^2 x} e ^{-\cos ^2 x}=- f (x) \\ \therefore & f (x) \text { is an odd function. } \\ \therefore & \int_{-\pi / 2}^{\pi / 2} f (x) d x=0\end{array}$

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

Let POR be a triangle of area $\Delta$ with $a =2$, $b =\frac{7}{2}$ and $c =\frac{5}{2}$, where $a, b$ and $c$ are the lenghts of the sides of the triangle opposite to the angles at $P, Q$ and $R$ respectively. Then $\frac{2 \sin P-\sin 2 P}{2 \sin P+\sin 2 P}$ equals

The solution of $\frac{d y}{d x}+ y =\cos x -\sin x$ is......

The order of the differential equation of all parabolas, whee latus rectum is $4 a$ and axis paralle! no the $x$-axis, is

The perpendicular distance of the plane $2 x+3 y-z=k$ from the origin is $\sqrt{14}$ units, the

value of k is

A circular sector of perimeter $60$ meter with maximum area is to be constructed. The radius of the circular arc in meter must be

A compound statement p →q is false only when

The area common to the parabola $y = 2x^2$ and $y = x^2+ 4$ is:

The value of $\int_{-1}^1 \frac{\sin x-x^2}{3-|x|} d x$ is

$\tan ^{-1}(\sqrt{3})-\cot ^{-1}(-\sqrt{3})$ is equal to

The general value of $\theta$ satisfying $\sin ^2 \theta+\sin \theta=2$ is