WorksheetAreasVolumesArcLengths

WorksheetAreasVolumesArcLengths -...

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AP Calculus AB Worksheet Areas, Volumes, and Arc Lengths Areas To find the area between the graph of f(x) and the x-axis from x = a to x = b we first determine if the function crosses the x-axis on the interval. If it does not cross the x-axis 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 x-axis 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 x-axis we find the area by integrating on the subinter- vals defined by the x-intercepts and adding the opposite of the integrals for any region that is under the x-axis. Note: When using your calculator you can take a shortcut when finding the area between the graph of a function and the x-axis by integrating the absolute value of f(x) on the interval in question. This results in the area between the curve and the x-axis because the graph of the absolute value of f(x) will lie entirely above the x-axis. 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. The height of a typical rectangular element will then be the top function minus the bottom function.
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WorksheetAreasVolumesArcLengths -...

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