_ - ,a ^a ,f ,(x) ,dx = - Vidyadip

MCQ

$\int\limits_{ - \,a}^a {\,f\,(x)\,dx} $=

✓
$\int\limits_0^a {\,\left[ {f\,(x)\,\, + \,\,f\,( - \,x)} \right]\,dx} $
B
$\int\limits_0^a {\,\left[ {f\,(x)\,\, - \,\,f\,( - \,x)} \right]\,dx} $
C
$2$ $\int\limits_0^a {\,f\,(x)\,dx} $
D
$Zero$

✓

Answer

Correct option: A.

$\int\limits_0^a {\,\left[ {f\,(x)\,\, + \,\,f\,( - \,x)} \right]\,dx} $

a
$I =$ $\int\limits_{ - \,a}^a {\,f\,(x)\,dx} $ =$\int\limits_{ - a}^a {f( - x)\,dx} $ (using $K$)
$\therefore$ $2I$ = $\int\limits_{ - \,a}^a {\,\left( {f\,(x) + f( - x)} \right)\,dx} $ =$2\,\int\limits_0^a {\,\left( {f\,(x) + f( - x)} \right)\,dx} $ (as integral is even)

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 "M.C.Q (1 Marks)" from STD 12 - 7.2 definite integral→STD 12 - 7.2 definite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Let $f : R \rightarrow R$ be a differentiable function with $f(0)=1$ and satisfying the equation $f(x+y)=f(x) f^{\prime}(y)+f^{\prime}(x) f(y)$ for all $x, y \in R$ Then, the value of $\log _c(f(4))$ is. . . . . .

$\int\limits^\pi_0\sqrt{\frac{1-\text{x}}{1+\text{x}}}\text{ dx}=$

If three conterminous edges of a parallelopiped are represented by $a - b,\,\,b - c$ and $c - a$, then its volume is

If $ a, b, c$ are non-coplanar unit vectors such that $a \times (b \times c) = \frac{{b + c}}{{\sqrt 2 }}$, then the angle between $a$ and $ b $ is

If $A = \left( {\begin{array}{*{20}{c}}1&2&0\\0&1&2\\2&0&1\end{array}} \right),$then $adj \,A$

Area of the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ is

The projection of the vector $\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ along the vector of $\hat{\text{j}}$ is:

The degree of the differential equation $\frac{{{d^2}y}}{{d{x^2}}} - \sqrt {\frac{{dy}}{{dx}} - 3} = x$ is

Three vectors $\vec a,\vec b,\vec c$ are inclined at an acute angle with each other such that $\left| {\vec a} \right| = 2\,,\,\left| {\vec b} \right| = 3\,,\,\left| {\vec c} \right| = 9$ and lengths of projection of $\vec a$ on $\vec b$ , $\vec b$ on $\vec c$ & $\vec c$ on $\vec a$ respectively are in geometric progression. If angles between $\vec a$ & $\vec b$ is $\frac {5\pi}{12}$ and between $\vec c$ & $\vec a$ is $\frac {\pi}{12}$ then the angle between $\vec b$ & $\vec c$ is

$\int_{}^{} {\frac{{{e^x}\;dx}}{{\sqrt {1 - {e^{2x}}} }} = } $