Integral Evaluation

Riemann Sum

1) Estimating the area under a curve with a graph

• Explanation:

2) Estimating the area under a curve with a function

• Explanation:

• Practice Problems

3) Estimating the area under a curve with a table

• Explanation:

• Practice Problems

4) Find the area under a curve when it is an exact geometric shape & Integral Notation

• Explanation:

• Practice Problems

5) Estimating the area under a curve using the Trapezoidal Rule

• Explanation:

• Practice Problems

6) Over and Under Estimates

• Explanation:

• Practice Problems

7) Integral Properties

• Explanation:

• Practice Problems

8) Review approximation methods and integral properties

• Practice Problems

9) First Semester Review

Antiderivatives and Indefinite Integrals

10) Basic antiderivatives (power rule; basic trig)

11) Review Basic antiderivatives

• Explanation:

• Practice Problems:

12) Particular Solution/Initial Value

13) U-Substitution with Indefinite Integrals with Powers

14) U-Substitution with Indefinite Integrals with Exponential and Trig

15) Mixed Review of Indefinite Integrals

• Practice Problems:

16) Double U-Sub

Definite Integrals: Fundamental Theorem of Calculus (FTC) - evaluation part:

17) Definite Integrals with antiderivative rules

• Explanation:

18) With U-Sub:

19) Using Definite Integrals with Integral Properties

• Explanation:

• Practice Problems:

20) Antiderivative of Derivatives

• Explanation:

• Practice Problems:

21) Integral of Piecewise functions

• Explanation

• Practice Problems

22) Using Your calculator to approximate definite Integrals

23) Average Value of a Function

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

26) Cumulative Review