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

Question

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

✓

Answer

c
(c) $I = \int_{ - \pi /2}^{\pi /2} {\frac{{\sin x}}{{1 + {{\cos }^2}x}}{e^{ - {{\cos }^2}x}}dx} $

$\because \frac{\sin x}{1+{{\cos }^{2}}x}{{e}^{-{{\cos }^{2}}x}}$ is an odd function,

$\therefore$ $I = 0$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\sum\limits_{ k =1}^{31}\left({ }^{31} C _{ k }\right)\left({ }^{31} C _{ k -1}\right)-\sum\limits_{ k =1}^{30}\left({ }^{30} C _{ k }\right)\left({ }^{30} C _{ k -1}\right)=\frac{\alpha(60 !)}{(30 !)(31 !)}$

Where $\alpha \in R$, then the value of $16 \alpha$ is equal to

Let $f$ be function such that $f(x + y) = f(x) + f(y)$ for all $x$ and $y$ and $f(x) = (2x^2 + 3x)g(x)$ for all $x$; where $g(x)$ is continuous and $g(0) = 3.$ Then $f '(x)$ is equal to :-

$ABCD$ is a rhombus. The circumradii of $\Delta ABD$ and $\Delta ACD$ are $\frac{25}{2}$ and $25$. Then the area of rhombus is .............. $\mathrm{sq. \,unit}$

The number of solutions of the equation $sin\, 2x - 2\,cos\,x+ 4\,sin\, x\, = 4$ in the interval $[0, 5\pi ]$ is

The sum of distinct values of $\lambda$ for which the system of equations

$(\lambda-1) x+(3 \lambda+1) y+2 \lambda z=0$

$(\lambda-1) x+(4 \lambda-2) y+(\lambda+3) z=0$

$2 x+(3 \lambda+1) y+3(\lambda-1) z=0$

has non-zero solutions, is

Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty

If $tan^{-1} (x+ 2)+ tan^{- 1}( x -2)= tan^{-1} (\frac{1}{2}),$ then sum of value(s) of $x$ is equal to-

If $A = \left[ {\begin{array}{*{20}{c}}4&2\\3&4\end{array}} \right]$,then $|adj\,\,A|$is equal to

The number of solution$(s)$ of the equation $ln(lnx)$ = $log_xe$ is -

If $\vec w = \alpha \left( {\vec a \times \vec b} \right) + \beta \left( {\vec b \times \vec c} \right) + \gamma \left( {\vec c \times \vec a} \right),$ $\left[ {\vec a,\vec b,\vec c} \right] = 2$ and $\vec w.\left( {\vec a + \vec b + \vec c} \right) = 8$, then $\alpha + \beta + \gamma =$