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Riemann Sum
Riemann Sum
1) Estimating the area under a curve with a graph
Explanation:
7) Integral Properties
Explanation:
Practice Problems
8) Review approximation methods and integral properties
Practice Problems
Antiderivatives and Indefinite Integrals
Antiderivatives and Indefinite Integrals
10) Basic antiderivatives (power rule; basic trig)
Explanation:
Trig Review Handout (includes trig identities, derivatives, and antiderivatives)
Videos:
Hollis: Antiderivative and Indefinite Integrals - slides 1-8
Practice Problems:
12) Particular Solution/Initial Value
Explanation
Video: Hollis: Antiderivative and Indefinite Integrals - slide 9
Practice Problems:
13) U-Substitution with Indefinite Integrals with Powers
Explanation:
Videos:
Hollis: Change of Variables (Substitution) - slides 1-7
Definite Integrals with U-Sub Kahn video - Indefinite Integration (part III) - more of an intuitive approach for reverse of the chain rule than using u-sub
Hollis: The Natural Log: - watch slides 6 and 7
Practice Problems:
14) U-Substitution with Indefinite Integrals with Exponential and Trig
Explanation:
Videos:
Hollis: The exponential function: watch slide 3 & 4
Practice Problems:
15) Mixed Review of Indefinite Integrals
16) Double U-Sub
Definite Integrals: Fundamental Theorem of Calculus (FTC) - evaluation part:
Definite Integrals: Fundamental Theorem of Calculus (FTC) - evaluation part:
18) With U-Sub:
Explanation:
Video:
Hollis: Change of Variables (Substitution) - slides 8-9
Practice Problems
19) Using Definite Integrals with Integral Properties
Explanation:
Practice Problems:
20) Antiderivative of Derivatives
Explanation:
Practice Problems:
22) Using Your calculator to approximate definite Integrals
23) Average Value of a Function
Explanation:
Practice Problems:
Desmos Activity: Average Value of a Function (teacher use only)
24) Integral Review
2012 Q1 - given a table: average rate of change, average value - parts a, b, and c
2011 (Form B) Q6 - part a: integral evaluation
2011(Form B) Q2 - given a piecewise function: average rate, instantaneous rate of change
2011 (Form B) Q1 - given a function: net change, average rate of change, existence
2011 Q6 - given a piecewise function: evaluate a definite integral
2010 Q2 - given a table and equation: average rate, average value
2009 Q5 - given a table: average rate, left Riemann sum
2008 (Form B) Q3 - given a table and equation: trap sum, average value, net change
2005 Q3 - given a table: average rate, average value, trap
2004 Q1 - given an equation: net change, average value, average rate
2003 (Form B) Q3 - given a table: average rate, midpoint sum
2003 Q3 - given a table and graph: rates, average value, left Riemann sum
2001 Q5 - part b - solve for a constant given a definite integral
2001 Q2 - given a table and equation: trap sum, average rate, average value, instantaneous rate
1999 Q3 - given a table and equation: midpoint sum, average value
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