Close your eyes and visualize a definite integral. An interactive provides a visualization of a function and definite integral on a closed interval. Pupils move one point of the interval in either the positive or negative direction....

Learning about definite integrals is fundamental to any calculus course. The eighth of 16 parts in Unit 6 - Integration focuses on the Fundamental Theorem of Calculus. Scholars first see how to find antiderivatives, then discover how to...

Properly apply the properties of integrals. By watching a video, scholars learn about the properties of definite integrals. They see how to use the area under a curve and the properties to determine the value of a given definite integral.

U is for u-substitution. Viewers of an instructional video learn how to apply u-substitution to determine integrals for more complex functions. They first find indefinite integrals, then move on to definite integrals.

Develop more than just a topical approach to the exam. The six free-response questions from 2006 reveal how the AP exam assesses topics. By using the questions, pupils practice topics such as velocity, sketch slope fields, solving...

Sometimes it's important to stop and take the time to review. Pupils look back at the second half of the unit and consider what they have learned about integration. They complete a instructional activity of review problems that assesses...

Accumulate the content so far. Learners review the content from the first five lessons dealing with accumulation functions. The eight problems go over finding maximums, minimums, concavity, points of inflection, and intervals of increase...

Calculus classes definitely need to learn about indefinite integrals. Individuals watch an informative video to learn the antiderivative rules for exponential, logarithmic, trigonometric, and inverse trigonometric functions. To solidify...

Finding the volume is an integral characteristic of a vase. Using the idea that summing the areas of cross-sectional disks will calculate the volume of a rotational solid, pupils find the volume of a vase. Scholars determine the interval...

Approximate the volume of a solid of revolution. Using a method similar to approximating the area under a curve, pupils investigate the volume of a solid of revolution. The learners use a given definite integral to find the volume of...

Sometimes close enough is appropriate. A curriculum document for AP® Calculus examines the importance of providing approximation questions throughout the course. It looks at approximating derivative values, approximating definite...

Differentiate between calculus concepts. The beginning of a helpful calculus resource begins with a short review of functions and moves right into limits to define derivatives. The six-chapter resource continues with applications of...

Here's the antidote to ignorance on antiderivatives. Pupils try a set of problems that require finding the antiderivative. They choose from different techniques they already know to determine the indefinite integral or the definite...

Delve into the middle of calculus. The resource is the second eBook of three that covers the complete calculus content. Seven chapters begin with integrals and different methods of integration before moving on to differential equations....

Connect integrals with differentiation. The beginning of the video introduces the definition of an accumulation function. Scholars learn about the relationship between integrals and derivatives. Using what is commonly known as Part Two...

This is integral to the test. Pupils realize that every question in the released free-response items from the 2008 AP® Calculus exam Form B requires integration. By reviewing the additional resources, scholars learn how important it is...

Let's put it in context. Pupils use the AP® Calculus BC free-response questions to practice for the exam. Five of the six released items deal with mathematical problems, with one using a real-world situation. Learners use differentiation...

How much work does it take to lift a bucket? An interactive presents a problem of lifting a bucket from the ground to the top of a building. Using their knowledge about work and integrals, pupils calculate the amount of work required to...

Discover another way to find the volume of a cone. Pupils explore how the area of a cross section changes as it moves through a cone. The interactive uses that knowledge to develop the integral to use to find the volume of the cone....

How would those items score? The resource provides pupils an opportunity to answer actual free-response questions and determine their scores. Items from the AP® Calculus AB exam from the 2008 administration demonstrate how topics appear...

Take another look at the exam. A set of questions is a different form for the 2004 AP® Calculus BC free-response question section. The questions are evenly split into calculator and non-calculator sections. Pupils use their knowledge of...

This textbook takes the learner from the basic definition of slope through derivatives, integrals, and vector multivariable calculus. Each section is composed primarily of examples, with theoretical introductions and explanations in...

Bingo! Combine the thrill of bingo with Lois Lowry's The Giver in a fun vocabulary lesson. Kids write selected vocabulary words from the novel onto a bingo chart, and then listen for the correct definitions in order to mark off...

What's on the test? Released items provide insight into the AP Calculus test. The six items are split into two groups, two calculator items and four non-calculator items. Resources allow teachers to see what kinds of answers test takers...