_ - 1 ^1 2 - x 2 + x ,dx = - Vidyadip

MCQ

$\int_{ - 1}^1 {\log \frac{{2 - x}}{{2 + x}}\,dx} = $

A
$2$
B
$1$
C
$ - 1$
✓
$0$

✓

Answer

Correct option: D.

$0$

d
(d) Let $f(x) = \log \left( {\frac{{2 - x}}{{2 + x}}} \right)$

$ \Rightarrow f( - x) = \log {\left( {\frac{{2 - x}}{{2 + x}}} \right)^{ - 1}} $

$= - \log \left( {\frac{{2 - x}}{{2 + x}}} \right) = - f(x)$

$\therefore $ $\int_{ - 1}^1 {\log \left( {\frac{{2 - x}}{{2 + x}}} \right)\,\,dx = 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

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

Similar questions

The equation of the normal to the curve x = a cos³ θ, y = a sin³ θ at the point $\theta=\frac{\pi}{4}$ is:

x = 0
y = 0
c = y
x + y = a

The order and degree of the differential equation ${\left( {1 + 3\frac{{dy}}{{dx}}} \right)^{\frac{2}{3}}} = 4\frac{{{d^3}y}}{{d{x^3}}}$ are

The region represented by the inequation system x, y ≥ 0, y ≤ 6, x + y ≤ 3 is:

unbounded in first quadrant
unbounded in first and second quadrants
bounded in first quadrant
none of these

Evaluate: $\int \frac{x^3-x^2+x-1}{x-1} d x$

The value of $\int \limits_{-2012}^{2012}\left(\sin \left(x^3\right)+x^5+1\right) d x$ is

The number of distinct real roots of $\left| {\,\begin{array}{*{20}{c}}{\sin x}&{\cos x}&{\cos x}\\{\cos x}&{\sin x}&{\cos x}\\{\cos x}&{\cos x}&{\sin x}\end{array}\,} \right| = 0$ in the interval $ - \frac{\pi }{4} \le x \le \frac{\pi }{4}$ is

If $A = \left[ {\begin{array}{*{20}{c}}0&i\\{ - i}&0\end{array}} \right]$, then the value of ${A^{40}}$ is

If the value of the integral $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{x^2 \cos x}{1+\pi^x}+\frac{1+\sin ^2 x}{1+e^{\sin x^{323}}}\right) d x=\frac{\pi}{4}(\pi+a)-2$, then the value of $a$ is

The value of the integral $\int \limits_1^2\left(\frac{t^4+1}{t^6+1}\right) d t$ is $..........$.

If $x\frac{{dy}}{{dx}} + y = x\frac{{f\left( {xy} \right)}}{{f'\left( {xy} \right)}}$ , then $f(xy)$ is equal to