3. In this question, you will find the exact value of $\int_0^5 \frac{x^2}{2} + 2xdx$ using Riemann sums
(a) Using the formulae in pg 218 of textbook, simplify $\sum_{i=1}^n \frac{i^2}{2}$ and $\sum_{i=1}^n 2i$.
(b) Approximate $\int_0^5 \frac{x^2}{2} + 2xdx$ via the Riemann sum, using the partition of [0, 5] into $n$ equal intervals, and using the right endpoint of each interval as the sample point. Your answer should depend on $n$ and use (a) to simplify. Let this Riemann sum be denoted $S_n$.
(c) Compute the limit $\lim_{n \to \infty} S_n$.
