Mark the correct alternative in each of the following: `int_0^1sqrt(x(1-x))dx` equals `pi//2` (b) `pi//4` (c) `pi//6` (d) `pi//8`

Explanation

`int_0^1sqrt(x(1-x))dx`

let `x=sin^2b`

so,`dx=2sinbcosbdb`

when `x=0` then `b=0`

when `x=1` then `b=(pi)/2`


thus,

`int_0^(pi)/2 sqrt(sin^2b cos^2b)2sinbcosbdb`
...