By using the properties of definite integrals, evaluate the integrals`int_0^(2) xsqrt(2-x)dx`

Explanation

Given,`I=∫_0^2x√(2-x) dx`

using property
`I=∫_0^af(x) dx=∫_0^af(a-x) dx`

`I=∫_0^2(2-x)√(2-(x-2)) dx`

`I=∫_0^2(2-x)√(2-x+2) dx`

`I=∫_0^2(2-x)√x) dx`

`I=∫_0^2(2-x)x^(1/2) dx`

`I=∫_0^2(2*x^(1/2)-x*x^(1/2))dx`

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