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Lecture

# 7.7 Approximate Integration: Overview

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School
University of Toronto St. George
Department
Mathematics
Course
MAT136H1
Professor
all
Semester
Winter

Description
7.7 Integration Techniques Integral Approximation: Overview For integrals where algebraic evaluation of the anti-derivative is difficult or even impossible, various approximation methods are used. Error Bounds All approximation methods result in small amount of error so that if it were added to the approximation, it equals the exact value of the integral. Sample Point Approximation ∫ ( ) ∑ [ ( ) ] , where is any point in the th subinterval[ ] If is chosen to be the left endpoint, then ( ) ∑ [ ( )] ∫ If is chosen to be the right endpoint, then∫ ( ) ∑ [ ( ) ] where for both, , and Midpoint Rule ∫ ( ) ∑ [ (̅) ] [ (̅̅̅ (̅̅̅ (̅̅̅)] , where , and ̅ is the mi
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