009B Sample Midterm 2, Problem 1

Consider the region $S$ bounded by $x=1,x=5,y={\frac {1}{x^{2}}}$ and the $x$-axis.

a) Use four rectangles and a Riemann sum to approximate the area of the region $S$. Sketch the region $S$ and the rectangles and indicate your rectangles overestimate or underestimate the area of $S$.

b) Find an expression for the area of the region $S$ as a limit. Do not evaluate the limit.

Foundations:
Link to Riemann sums page

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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