_ ^ dx 2x - x^2 = - Vidyadip

MCQ

$\int_{}^{} {\frac{{dx}}{{\sqrt {2x - {x^2}} }} = } $

A
${\cos ^{ - 1}}(x - 1) + c$
✓
${\sin ^{ - 1}}(x - 1) + c$
C
${\cos ^{ - 1}}(1 + x) + c$
D
${\sin ^{ - 1}}(1 - x) + c$

✓

Answer

Correct option: B.

${\sin ^{ - 1}}(x - 1) + c$

b
(b)$\int_{}^{} {\frac{{dx}}{{\sqrt {2x - {x^2}} }}} = \int_{}^{} {\frac{{dx}}{{\sqrt {1 - {{(x - 1)}^2}} }}} = {\sin ^{ - 1}}(x - 1) + c.$

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