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STD 12 - 7.2 definite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.2 definite integral4 Marks
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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