The integrals of exponential functions are found in these examples and exercises. Students have and opportunity to solve the problems prior to seeing the solutions.

This site provides a detailed overview of the various methods of integration. This first page covers the "gist" of the methods available, followed by much more detail on subsequent pages.

Formulas are presented for several types of integrals that contain trigonometric functions. Examples are provided to allow students to practice applying the formulas. Solutions are provided with step-by-step details.

In this activity, students examine functions defined by a definite integral. They create tables and graphs for integration functions. They understand the foundation of the Fundamental Theorem of Calculus.

In this activity, students learn and explore how Indefinite integrals are used to find the antiderivative of a function. They also learn that Definite integrals can be used to find the area bounded by a function and the X-axis. From...

This activity allows the user to find the volume and surface area of various functions as they are rotated around axes. This applet can be used to practice finding integrals using the disk and washer methods of calculating volume.

The resource examines applications of integration. Topics investigated are arc length, surface area, center of mass, hydrostatic pressure, and probability density functions. Class notes, definitions, and examples with detailed solutions...

This activity will show a function with rectangle areas on the graphing calculator.

In this activity, students explore the connection between an accumulation function, one defined by a definite integral, and the integrand. They also discover that the derivative of the accumulator is the integrand.

Learn about the fundamental theorem of calculus with this helpful reference tool. Provides a detailed definition and examples that enhance further explanation. Includes links to related topics.

[Free Registration/Login Required] Two different techniques for integrating composite functions, pattern recognition and change of variables, are discussed using a process called u-substitution. This pattern recognition uses both of the...

This page discusses the Leibniz Integral Rule, which concerns "the differentiation of a definite integral whose limits are functions of the differential variable."

This tutorial takes a look at using definite integrals to determine the average value of a function on an interval and also the Mean Value Theorem for integrals.

This site has the definition of average of a function by using integrals. The site also contains the proof of the mean value theorem which may be viewed one step at a time. There are links to related exercises whose answer is shown one...

Draw a graph of any function and see graphs of its derivative and integral. Don't forget to use the magnify/demagnify controls on the y-axis to adjust the scale.

Good site with many of the elliptic functions given.

Students explore the definition of a function by playing an interactive game called "Club Function." The goal of the game is to be in the club! With students each assigned to be either a zebra or a rhinoceros, they group themselves...

Students teams design and build shoe prototypes that convert between high heels and athletic shoes. They apply their knowledge about the mechanics of walking and running as well as shoe design (as learned in the associated lesson) to...

In this lesson the learners will learn how the heart functions. Students will be introduced to the concept of action potential generation. The lesson will explain how action potential generation causes the electrical current that causes...

Through two lessons and five activities, students explore the structure and function of cell membranes. Specific transport functions, including active and passive transport, are presented. In the legacy cycle tradition, students are...

This site is a wonderful exercise for students with a Calculus base. The site gives an interactive drawing of a vase where the measurements of the diameter of the vase are at any point. The student then finds the volume using calculus....

Students model and design the sound environment for a room. They analyze the sound performance of different materials that represent wallpaper, thick curtains, and sound-absorbing panels. Then, referring to the results of their analysis,...

Young scholars take a closer look at cars and learn about some characteristics that affect their energy efficiency, including rolling resistance and the aerodynamics of shape and size. They come to see how vehicles are one example of a...

This lesson culminates the unit with the Go Public phase of the legacy cycle. In the associated activities, students use linear models to depict Hooke's law as well as Ohm's law. To conclude the lesson, students apply they've learned...