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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
Let $\int\limits_0^1 {{{\tan }^{ - 1}}\left( {\frac{{\tan x}}{2}} \right)} dx = \alpha $ then $\int\limits_0^1 {{{\tan }^{ - 1}}\left( {\frac{{\tan x - 2\cot x}}{3}} \right)} dx$ is
  • A
    $\pi  - \alpha  + \frac{1}{2}$
  • B
    $\alpha  - \frac{\pi }{2} - 1$
  • C
    $\alpha  + \pi  - 1$
  • ✓
    $\alpha  - \frac{\pi }{2} + \frac{1}{2}$
✓

Answer

Correct option: D.
$\alpha  - \frac{\pi }{2} + \frac{1}{2}$
d
$\int_{0}^{1} \tan ^{-1}\left(\frac{\tan x}{2}\right) d x-\int_{0}^{1} \tan ^{-1}(\cot x) d x$

$\alpha-\int_{0}^{1}\left(\frac{\pi}{2}-x\right) d x$

$\alpha-\frac{\pi}{2}+\frac{1}{2}$

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