Question

I am having some trouble with a simple integration

Answer 1

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

Answer 2

Let's expand the integrand\[\int\limits_a^b x (b^2 - 2xb + x^2) dx = \int\limits b^2x dx - \int\limits 2x^2b dx+ \int\limits x^3 dx\] The limits are the same.

Answer 3

\[0.5 b^2 x^2 |_a^b - (2/3)bx^3 |_a^b + (1/4)x^4 |_a^b\]

Answer 4

\[= \frac{1}{(b-a)^2}\left(\left.\frac{b^2x^2}{2}-\frac{2}{3}bx^3+\frac{x^4}{4} \right|_a^b\right)\]
\[\]

Answer 5

then take out the 1/12 ?

Answer 6

* x^2/12

Answer 7

my laptop is about to run out of battery
thanks for assistance, ill be back tomorrow to work on this