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

Question

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

✓

Answer

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

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

Similar questions

The number of $3$-$digit$ odd numbers, whose sum of digits is a multiple of $7$ , is

Equation of two diameters of a circle are $2 x-3 y=5$ and $3 x-4 y=7$. The line joining the points $\left(-\frac{22}{7},-4\right)$ and $\left(-\frac{1}{7}, 3\right)$ intersects the circle at only one point $P(\alpha, \beta)$. Then $17 \beta-\alpha$ is equal to

If two perpendicular rays from focus of parabolic surface $y^2 = 4x$ are incident at points $A(t^2_1,2t_1)$ & $A(t^2_2,2t_2)$ such that $t_1t_2 = -10$, then distance between the reflected rays will be -

For the two positive numbers $a , b$, if $a , b$ and $\frac{1}{18}$ are in a geometric progression, while $\frac{1}{ a }, 10$ and $\frac{1}{ b }$ are in an arithmetic progression, then, $16 a+12 b$ is equal to $.........$.

Let $\overrightarrow{ c }$ be a vector perpendicular to the vectors $\overrightarrow{ a }=\hat{ i }+\hat{ j }-\hat{ k }$ and $\overrightarrow{ b }=\hat{ i }+2 \hat{ j }+\hat{ k }.$

If $\overrightarrow{ c } \cdot(\hat{ i }+\hat{ j }+3 \hat{ k })=8$ then the value of $\overrightarrow{ c } \cdot(\overrightarrow{ a } \times \overrightarrow{ b })$ is equal to ...... .

$2{\cos ^2}\theta - 2{\sin ^2}\theta = 1$, then $\theta =$ .......$^o$

Let the length of the focal chord $P Q$ of the parabola $y^2=12 x$ be $15$ units. If the distance of $P Q$ from the origin is $\mathrm{p}$, then $10 \mathrm{p}^2$ is equal to....................

Let $S = \left\{ {\left( {\begin{array}{*{20}{c}}
{{a_{11}}}&{{a_{12}}}\\
{{a_{21}}}&{{a_{22}}}
\end{array}} \right):{a_{ij}} \in \left\{ {0,1,2} \right\},{a_{11}} = {a_{22}}} \right\}$ Then the number of non-singular matrices in the set $S$ is

If $(x + 1)$ is a factor of ${x^4} - (p - 3){x^3} - (3p - 5){x^2}$ $ + (2p - 7)x + 6$, then $p = $

The number of values of $x$ in the interval $[0, 5 \pi ] $ satisfying the equation $3{\sin ^2}x - 7\sin x + 2 = 0$ is