# 007B Sample Midterm 1, Problem 1

Let  ${\displaystyle f(x)=1-x^{2}}$.
(a) Compute the left-hand Riemann sum approximation of  ${\displaystyle \int _{0}^{3}f(x)~dx}$  with  ${\displaystyle n=3}$  boxes.
(b) Compute the right-hand Riemann sum approximation of  ${\displaystyle \int _{0}^{3}f(x)~dx}$  with  ${\displaystyle n=3}$  boxes.
(c) Express  ${\displaystyle \int _{0}^{3}f(x)~dx}$  as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.