This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Calculus Worksheet Areas and Volumes Areas To find the area between the graph of f(x) and the xaxis from x = a to x = b we first determine if the function crosses the xaxis on the interval. If it does not cross the xaxis and f(x) > 0 on the interval then the area is given by Area = Ÿ a b f H x L ‚ x If the graph of f does not cross the xaxis and f(x) < 0 on the interval then the area is given by Area =  Ÿ a b f H x L ‚ x If the graph of f crosses the xaxis we find the area by integrating on the subintervals defined by the xinter cepts and adding the opposite of the integrals for any region that is under the xaxis. Note: When using your calculator you can take a shortcut when finding the area between the graph of a function and the xaxis by integrating the absolute value of f(x) on the interval in question. This results in the area between the curve and the xaxis because the graph of the absolute value of f(x) will lie entirely above the xaxis. To find the area between two curves we find the points of intersection. If they intersect in only two points then one of the functions will dominate the other on that interval. one of the functions will dominate the other on that interval....
View
Full
Document
This note was uploaded on 04/15/2011 for the course MATH 1400 taught by Professor Grether during the Spring '08 term at North Texas.
 Spring '08
 Grether
 Calculus

Click to edit the document details