Q51 / 150 · MHT CET 2020 (12 Oct Shift 1) · Mathematics

$$ \int \frac{d x}{\sqrt{5+4 x-x^{2}}}= $$

  • Correct answer
    A
    $\sin ^{-1}\left(\frac{x-2}{3}\right)+c$
  • B
    $\log \left|(x-2)+\sqrt{5+4 x-x^{2}}\right|+c$
  • C
    $\log \left|(x+2)+\sqrt{5+4 x-x^{2}}\right|+c$
  • D
    $\sin ^{-1}\left(\frac{x+2}{3}\right)+c$

Solution

$I=\int \frac{d x}{\sqrt{9+\left(-4+4 x-x^{2}\right)}}=\int \frac{d x}{\sqrt{(3)^{2}-(x-2)^{2}}}=\sin ^{-1}\left(\frac{x-2}{3}\right)+c$

Hence, the correct answer is option: 'A'.

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