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Lecture

# 5.3 Integration & Anti-derivatives The Fundamental Theorem of Calculus Question #1 (Easy)

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

Description
5.3 Integration & Anti-derivatives The Fundamental Theorem of Calculus Question #1 (Easy): Evaluating the Integral Based on the Graph Strategy This is a simple calculation and reasoning exercise where the Fundamental Theorem of Calculus is not directly applied. However, it works as a foundation where the change in the area under the curve is linked to the anti-derivative of the curve. This helps to better understand the theoretical concept of the Fundamental Theorem of Calculus. Sample Question Let ( ) ∫ ( ) where the graph of is shown. 1) Evaluate ( ), ( ) and ( ). 2) Estimate ( ) for , and . 3) On what interval is increasing? 4) Where does have a maximum value? 5) Sketch a rough graph of . Solution 1) At ( ) ∫ ( )
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