Area Volume Review.notebook
April 14, 2017
Apr 14­8:27 AM
1
Area Volume Review.notebook
April 14, 2017
Apr 12­11:31 AM
2
Area Volume Review.notebook
April 14, 2017
Riemann Sums
*You might not have the same width on rectangles!*
Left sum­add the areas of the rectangles using the left endpoint for the height of the rectangle
Right sum­add the areas of the rectangles using the right endpoint for height of the rectangle
Midpoint sum­add the areas of the rectangles using the midpoint (of your width) value as the height of the rectangle
Trapezoidal sum­add the areas of the trapezoids (add left and right endpoints and divide by 2 for height)
Upper Sum­A sum that is an overestimate; which ever endpoint is taller (right sum for increasing, left endpoint for decreasing functions)
Lower Sum­A sum that is an underestimate; whichever endpoint is shorter, (left endpoint for increasing functions, right endpoint for decreasing functions)
Apr 10­9:50 AM
3
Area Volume Review.notebook
April 14, 2017
Area between two curves
1. Bounds are points of intersection.
2a) x­bounds, x­
variables (top­
bottom)
or
2b) y­bounds, y­
variables(right­left)
Apr 10­10:02 AM
4
Area Volume Review.notebook
April 14, 2017
Apr 13­1:38 PM
5
Area Volume Review.notebook
April 14, 2017
Apr 14­9:00 AM
6