Consider the function $\displaystyle f(x) = \frac {x^2}{2} + 9$.

In this problem you will calculate $\displaystyle \int_{0}^{3} \left( \frac {x^2}{2} + 9 \right) \,dx$ by using the definition $$\int_{a}^{b} f(x) \,dx = \lim_{n \to \infty} \left[ \sum_{i=1}^{n} f(x_i) \Delta x \right]$$

The summation inside the brackets is $R_n$ which is the Riemann sum where the sample points are chosen to be the right-hand endpoints of each sub-interval.

Calculate $R_n$ for $\displaystyle f(x) = \frac {x^2}{2} + 9$ on the interval $[0, 3]$ and write your answer as a function of $n$ without any summation signs. You may need the summation formulas available in the hint (which becomes available after you have submitted an answer).
$R_n =$
$\displaystyle \lim_{n \to \infty} R_n =$

Hint: