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Question

Question: \(\int _ { 1 / 4 } ^ { 1 / 2 } \frac { d x } { \sqrt { x - x ^ { 2 } } } =\)...

1/41/2dxxx2=\int _ { 1 / 4 } ^ { 1 / 2 } \frac { d x } { \sqrt { x - x ^ { 2 } } } =

A

π\pi

B

π2\frac { \pi } { 2 }

C

π3\frac { \pi } { 3 }

D

π6\frac { \pi } { 6 }

Answer

π6\frac { \pi } { 6 }

Explanation

Solution

=[sin1(2x1)]1/61/2=π/6= \left[ \sin ^ { - 1 } ( 2 x - 1 ) \right] _ { 1 / 6 } ^ { 1 / 2 } = \pi / 6 .