Math 161 Calculus I

Reading Outlines

You should answer these questions as you read the text.

Section 5.5

1. Will an approximating sum using 8 subdivisions of the interval [a, b] always be a closer approximation to $\int_{a}^{b}$f (x) dx than one using only 4 subdivisions? Explain.
2. Why might approximating sums (instead of exact integrals) be necessary in applications?
3. How can integrals be used to find areas between curves?
4. Give an example of an applied question in which you might want to find the area between two curves.
5. Find the area between the curves y = x² and y = 1, between their two points of intersection.
6. Why might it sometimes be convenient to integrate with respect to y instead of x?