009B Sample Midterm 1, Problem 5

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.

Foundations:
Link to Riemann sums content page

Solution:

Step 1:

Step 2:

Final Answer:

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