Evaluate the following integral:`int_0^2x\ sqrt(2-x)\ dx`

Explanation

Given:`int_0^2x\ sqrt(2-x)\ dx`

`I=int_0^2x\ sqrt(2-x)\ dx`

`I=int_0^2 (2-x)sqrtx dx`

`I=int_0^2 (2sqrtx-x^(3/2))dx)`

`I=2(x^(3/2))/(3/2)int_0^2 (-x^(5/2))/(5/2)|_0^2`

`I=4/3xx2sqrt2-2/5 4sqrt2`

`I=8/3sqrt2-8/5sqrt5`

`I=(16sqrt2)/15`