The goal of this exercise is to approximate the value of the definite integral $\int_1^3 (x^2 - 1)dx$ using a Riemann sum with right endpoints and 8 subintervals (i.e. using the Riemann sum $R_8$).
a) If you sub-divide the interval $[1, 3]$ into 8 subintervals of equal length $\Delta x$, you get 8 subintervals of the form $[x_{i-1}, x_i]$ whose union is the interval $[1, 3]$. Find the endpoints $x_0, x_1, \dots, x_8$ that define these 8 subintervals.
FORMATTING: To enter your answer, list the endpoints in the form $[x_0, x_1, \dots, x_8]$ including the square brackets [] and a comma (,) between endpoints. The endpoints should be exact numbers, ordered from left to right.
Answer: $[x_0, x_1, \dots, x_8] =$
b) Compute the exact value of each term $t_i = f(x_i)\Delta x$ of the Riemann sum $R_8$.
FORMATTING: To enter your answer, list the terms in the form $[t_1, t_2, \dots, t_8]$ including the square brackets [] and a comma (,) between consecutive terms. Each term must be an exact number. The terms must be ordered from left to right.
Answer: $[t_1, t_2, \dots, t_8] =$
c) Compute the value of the Riemann sum $R_8$. Write your answer with an accuracy of two decimal places.
Answer: Number
