UNIT 5: Integration
Objectives: Upon completion of the unit, students will be able to:

Estimate the area under a curve using rectangles (lower and upper estimates)
 Approximate the area under the curve using either a table or graph and label appropriately
 Write the definition of the integral using the limit and evaluate the limit using the limit sums given
 Determine a definite integral using the properties of integration
 Find the definite integral value on the graphing calculator
 Determine a general antiderivative



Find a particular solution to a differential equation
Determine the antiderivative using u-substitution
Understand and apply the *two* Fundamental Theorem of Calculus
Video Lectures
1a. Sigma notation
Video Examples
1a. Find area under function using 4 rectangles (left
endpoints)
1b. Area under curve
1b. Find area under function using 4 rectangles (right
endpoints)
1c. (from section 4.9 really)–Antiderivatives
1c. Approximate an area under a curve using rectangles
Section from
Text
(WebAssign)
5.1
1d. Intrepret the meaning of the area under a curve
2a. Riemann Sums and the Definite
Integral – setting up the integral using the
limit (part I and part II)
2a. Understanding the definition of the definite integral
5.2
2b. The Definite Integral
2b. Application of the definite integral - distance
3a. Fundamental Theorem of Calculus
Part I
3b. Fundamental Theorem of Calc Part II
3a. Find the definite integral using a calculator
5.3
4a. Determine the antiderivative
4a. Antiderivatives of trig functions
4b. Find the particular solution to a differential equation 5.4
5a. U substitution integration patrickjmt
5a. U substitution example - patrickjmt
5b. The 6 basic trig function
antiderivatives
5b. U substitution with trig (Part I and Part II)
5c. More U-Substitution - patrickjmt
5.5