THE DEFINITE INTEGRAL

Indefinite Integrals and Antiderivatives

Problems finding antiderivatives

Indefinite integrals problems, solutions, and explanations

Introduction to integrals
Intuitively understanding the integral applet
Indefinite Integrals

More on indefinite integrals
Even more on indefinite integrals

Antiderivatives from slope and the indefinite integral plotter

Basic antiderivatives applet

Antiderivatives and Slope Fields

Pictures of slope fields for parametrically defined derivatives

Pictures of slope fields of first order differential equations
Slope fields applet
Slope fields plotter
Another slope fields plotter

Graph solutions to differential equations applet
Slope Fields discussion

More discussion and exercises
Even more discussion

Instructions for using your calculator to graph a slope field

Area

The algebra of summation notation

Some special summations
Sigma Detectives worksheet to use in preparation for definite integral
Review of summation notation and formulas

Tool for finding area under a curve using rectangles

Rectangle Approximation Method applet
Approximations of areas
Area problems, solutions, and explanations
Area under a curve

Midpoint and trapezoidal Riemann sums applet

Definite Integrals applet

Properties of definite integrals applet

Riemann Sum applet
Maglev Train worksheet to use in preparation for definite integral
The limit definition of an integral
Review problems for finding area under a curve, using an integral--Go to Calculus Book I, then Applications of Integration, then Area Under a Curve

Riemann Sums and Definite Integrals

Riemann Sums

Riemann Sums applet
Riemann Sums applet
Riemann Sums and Definite Integrals
Riemann Sums plotter

Barehands Integration Worksheet

Series, Integrals, and Hidden Patterns Worksheet

Archimedes Approximation of pi (slides)

Another Archimedes Approximation site

The definite integral

The definite integral represented as area between a curve and the x-axis applet

The importance of the constant of integration
Review problems for setting up integrals as Riemann Sums--Go to Calculus Book I, then Integration, then Sums, then Riemann Sums

Fundamental Theorem of Calculus

Fundamental Theorem of Calculus applet

Second fundamental theorem applet

Meaning of Fundamental Theorem

Laws of integrals

Properties of Integrals

Draw the integral of a function
Find the error
Review problems for finding the average value of a function--Go to Calculus Book I, then Applications of Integration, then Average Value of a Function

Definition of Definite Integral and FTA problems, solutions, and explanations
Computing Definite Integrals and FTA problems, solutions, and explanations

Integration by Substitution

u-substitution applet

Another u-substitution applet
Integration by substitution applet

u-substitution

Problems using u-substitution
Problems with examples using u-substitution
Discussion on integration by substitution with examples
More on substitution
Substitution problems, solutions, and explanations
More substitution problems, solutions, and explanations
Substitution with definite integrals problems, solutions, and explanations
Integration by Substitution

Review problems for computing indefinite integrals with and without substitution--Go to Calculus Book II, then Chapter 1: Integration, then Section 2: Indefinite Integrals. Modules 1 - 4 have good problems to try. Also Section 3: Definite Integrals, Modules 1,2, and 3 is a good place to work.
Find the error
Find another error

Numerical Integration

Numerical Integration -- several methods

Trapezoidal Rule and Simpson's Rule
Trapezoidal Rule and Simpson's Rule applet
Trapezoidal Rule and Simpson's Rule as numerical approaches
Trapezoidal Rule
All numerical methods plotter

Surface Area of a Pool Problem
Review problems for approximating integrals, using the midpoint rule, the trapezoidal rule, and Simpson's rule--Go to Calculus Book I, then Integration, then Definite Integrals, then Lessons 3,4,5

Summaries and Review Problems
- Computing Integrals problems, solutions, and explanations
- Proofs of properties, FTA, MVT, etc