The function F(x) = _0^x ( 1 - x 1 + x ) ,dx is - Vidyadip

MCQ

The function $F(x) = \int_0^x {\log \left( {\frac{{1 - x}}{{1 + x}}} \right)} \,dx$ is

✓
An even function
B
An odd function
C
A periodic function
D
None of these

✓

Answer

Correct option: A.

An even function

a
(a) We know that if $f(t)$ is an odd function, then $\int_0^x {f(t)} $ $dt$ is an even function.

since the function here $f(x) = \log \frac{{1 - x}}{{1 + x}}$ is an odd function,

therefore $F(x)$ is an even function.

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

$\int_{}^{} {\frac{{dx}}{{\sqrt {1 + x} + \sqrt x }} = } $

The sum of coefficients in ${(1 + x - 3{x^2})^{2134}}$ is

If $\sum_{k=1}^{10} \frac{k}{k^{4}+k^{2}+1}=\frac{m}{n}$, where $m$ and $n$ are coprime, then $m+n$ is equal to.

$\int_{}^{} {\frac{1}{{1 + {{\cos }^2}x}}dx} = $

If the line $y = 2x + k$ is a tangent to the curve ${x^2} = 4y$, then $k$ is equal to

If $|x|<1,|y|<1$ and $x \neq y,$ then the sum to infinity of the following series $(x+y)+\left(x^{2}+x y+y^{2}\right)+\left(x^{3}+x^{2} y+x y^{2}+y^{3}\right)+\ldots .$

If $\tan \theta = \frac{{ - 4}}{3},$ then $\sin \theta = $

Let $A(2,3,5)$ and $C(-3,4,-2)$ be opposite vertices of a parallelogram $A B C D$ if the diagonal $\overrightarrow{B D}=\hat{i}+2 \hat{j}+3 \hat{k}$ then the area of the parallelogram is equal to

A tangent $P T$ is drawn to the circle $x^2+y^2=4$ at the point $P(\sqrt{3}, 1)$. A straight line $L$, perpendicular to $P T$ is a tangent to the circle $(x-3)^2+y^2=1$.

$1.$ A common tangent of the two circles is

$(A)$ $x=4$ $(B)$ $y=2$ $(C)$ $x+\sqrt{3} y=4$ $(D)$ $x+2 \sqrt{2} y=6$

$2.$ A possible equation of $L$ is

$(A)$ $x-\sqrt{3} y=1$ $(B)$ $x+\sqrt{3} y=1$ $(C)$ $x-\sqrt{3} y=-1$ $(D)$ $x+\sqrt{3} y=5$

Give the answer question $1$ and $2.$

$(z + a)(\bar z + a)$, where $a$ is real, is equivalent to