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.

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