Consider the function 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 isR_n which is the Riemann sum where the sample points are chosen to be the right-hand endpoints of each sub-interval.

CalculateR_n for 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.

R_n =

\displaystyle \lim_{n \to \infty} R_n =

In this problem you will calculate

The summation inside the brackets is

Calculate

You can earn partial credit on this problem.