Originally Posted by

**cathrinbleu** I do not understand the final step taken to solve this problem (It was an example given in class) I would really appreciate it if someone would be able to explain the simplification process for the final step?

f(x) = x^{n}

for

n ≥ 0, [0, 2]

$\displaystyle {\frac{1}{2-0} }\int\limits_{0}^{2}$x^{n}${dx}$ = $\displaystyle {\frac{1}{2n + 2}$x^{n+1}$ \Bigr\rvert\biggr \limits_{0}^{2}$

I understand that one must solve using the given limits, which would give me a value of:

$\displaystyle \biggl[{\frac{1}{2n + 2}$2^{n+1}$ \biggr]$ - $\displaystyle \biggl[{\frac{1}{2n + 2}$0^{n+1}$ \biggr] $

However, I am not following the what happens in order to have the final solution of:

$\displaystyle {$2^{n}$\frac{1}{n+1}}$

I end up with my final solution being: $\displaystyle {\frac{1}{2n + 2}$2^{n+1}$ $