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Lecture

# 5.2 Integration & Anti-derivatives Definite Integrals Question #1 (Easy)

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

Description
5.2 Integration & Anti-derivatives Definite Integrals Question #1 (Easy): Riemann Sum Using the Midpoints Strategy Riemann sum using the midpoints as sample points are calculated as: ∑ ̅ , where the midpoint for each subinterval is determined by ̅ . Riemann sum represents the sum of all the rectangles under the curve. Midpoints always present the best estimate. For increasing functions, left endpoints are associated with the lower estimate, and the right endpoints the upper estimate. Likewise, for decreasing functions, vice versa, meaning the left endpoints give the upper estimate and the right endpoints the upper estimate. Sample Question 1) Find the Riemann sum for , with . Take the midpoints as the sample points. 2) What does the Riemann sum represent? Solution mea
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