Question

\[ \frac{1}{{(b-a)}^2} \int\limits_{a}^{b}x(b-x)^2 \text{d} x\]

Answer 1

\[\text{let}\quad u=(b-x)^2\]\[\qquad\text{d}u=-2(b-x)\text{d}x\]

Answer 2

...

Answer 3

\[\frac{1}{{(b-a)}^2} \int\limits_{a}^{b}(xb^2+x^3 - 2bx^2) \text{d} x\]