Question

The function $F ( x ) = \int _ { 0 } ^ { x } \log \left( \frac { 1 - x } { 1 + x } \right) d x$ is

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

Answer 1

Answer: (A)

An even function

Answer 2

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.