Math 161 Calculus I

Reading Outlines

You should answer these questions as you read the text.

Section 5.4

1. Why would we want to calculate area under a curve by summing up sums of areas of rectangles or trapezoids?
2. What kind of sum do you think best approximates the true area under the curve? Is it always the best?
3. Does it matter what kind of sum you use? Why or why not?
4. Explain why the trapezoid approximation is the average of the left and right approximations.
5. Write out all the terms in the sum $$\sum_{k=1}^{4}$$k². Calculate this sum.
6. Do the same for the sum $$\sum_{j=1}^{5}$$f (j) where f (x) = x/2.
7. In the limit definition of the integral, what is going to infinity and what is going to zero?