Evaluate: ∫ x^2 (3 - x)^5/2 .dx, x ∈ [0,3]

Question

 Evaluate:

\(\int_0^3 x^2(3-x)^{5/2}.dx\)

∫ x² (3 - x)^5/2 .dx, x ∈ [0,3]

Answer 1

Let \(I\) = \(\int_0^3 x^2(3-x)^{5/2}.dx\)

We use the property

Here, a =3

Hence, in \(I\), changing x to 3-x,  we get