009B Sample Midterm 1, Problem 1

Let  $f(x)=1-x^{2}$.

(a) Compute the left-hand Riemann sum approximation of  $\int _{0}^{3}f(x)~dx$  with  $n=3$  boxes.

(b) Compute the right-hand Riemann sum approximation of  $\int _{0}^{3}f(x)~dx$  with  $n=3$  boxes.

(c) Express  $\int _{0}^{3}f(x)~dx$  as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.

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