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# Areas and Distances, Definite Integral

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## carly cooke

on 25 February 2013

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#### Transcript of Areas and Distances, Definite Integral

Areas and Distances,
Definite Integrals Left Hand Estimate Example:
f(x)= x²^2 [2,8]
using 3 rectangles Right Hand Estimate Midpoint the area of the integral from a to b equal f(x)dx Example:
f(x)= x^2² [2,8]
using 3 rectangles where x1, x2, x3, ... , xn are the midpoints of the n rectangles Example:
F(x)= x²^2 [2,8]
using 3 rectangles Properties of the Integral Trapezoidal area of a trapezoid= 1/2 (B1+B2) h Average of the left Riemann sum and right Riemann sum Example:
f(x)= x^2 [2,8]
using 3 rectangles High Estimate Low Estimate A Riemann sum is a method for approximating the total area underneath a curve on a graph, otherwise known as an integral.
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