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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int_0^{2a} {\frac{{f(x)}}{{f(x) + f(2a - x)}}\,dx = } $
  • ✓
    $a$
  • B
    $\frac{a}{2}$
  • C
    $2a$
  • D
    $0$
✓

Answer

Correct option: A.
$a$
a
(a) $I = \int_0^{2a} {\frac{{f(x)}}{{f(x) + f(2a - x)}}dx} $.....$(i)$

$I = \int_0^{2a} {\frac{{f(2a - x)}}{{f(2a - x) + f(x)}}\,} dx$.....$(ii)$

Adding $(i)$ and $(ii),$ we get 

$2I = \int_0^{2a} {\,\,dx = 2a \Rightarrow I = a} $.

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