Definite Integral Teacher Resources

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...

Here's an AP Calculus video that provides a discussion on determining an approximate for the area under a curve by calculating the sum of areas of rectangles that is smaller than the area and by finding the sum of areas of...

Young scholars identify the meaning of the Mean Value Theorem. In this calculus lesson, students solve problems using the definite integral. They calculate the average value of a function.

Students discuss the importance of fundamental theorems in math. For this calculus lesson, students define the fundamental theorem of calculus and discuss why it is so important they understand it. They work problems to model how this...

Students define integrals and explore how they relate to the areas under a curve. In this calculus lesson, students solve word problems relating curves and integrals. They sing a song to help them remember the formula for the area under...

Students evaluate and define limits using substitution. In this calculus lesson, students apply the use of Integrals to explore Newton's law of Cooling. They solve rate and temperature problems using Integrals.

In this college level calculus activity, students evaluate the given definite integrals.  The three page activity contains eight problems.  Solutions are not provided. 

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.

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...

Provide your students with a framework for introducing indefinite integrals. It takes into account a learner’s prior knowledge of slope fields and definite integrals and uses the notion of an antiderivative to give them an intuitive...

In this math worksheet, students determine if the definite integral of given functions exist. They use a Taylor polynomial to approximate given values. Students express the arc length of a graph on a polar coordinate system as an integral.

In this integral instructional activity, students sketch functions and use their graph to evaluate functions. This two-page instructional activity contains four multi-step problems.

If only there was a reference that listed all the formulas covered in calculus. Luckily, there is. This comprehensive 197-page handbook provides formulas and explanations for all topics in AP Calculus or in a standard college calculus...

Hands-on investigation of Riemann sums becomes possible without intensive arithmetic gymnastics with this interactive lesson plan. Learners manipulate online graphing tools to develop and test theories about right, left, and...

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...

So this is the real test? The resource provides the free-response questions from the 2011 AP Calculus AB exam. The six questions are split into two sections, calculator and non-calculator items. Several resources give teachers...

Apply the skills to problems to ace the AP test. Free-response questions require scholars to take calculus skills and apply them to situations. Pupils use the questions to see how those situations appear on an upcoming exam. Teacher use...

How much of the material is really important? Pupils use the free-response questions from the 2014 AP Calculus BC exam to see how the questions appear. With the supporting material, teachers understand the topics that appear on the test...

Pupils interact with six released questions from the 2018 AP Calculus AB exam. Teachers use the additional materials to determine where the class is in terms of readiness for the exam to help provide additional instruction as needed.

What is the answer to this question? Pupils use six questions to practice for the AP Calculus AB test. The review questions are divided in two sections, calculator and non-calculator. Additional resources allow teachers to determine how...

Using the common errors and test taker responses, it's easy for teachers to see where to pinpoint instruction throughout the AP Calculus course. Pupils, using the released items, develop an understanding of how future exams assess the...

How will the topics be assessed? Using the six released items from the Calculus AB test, pupils see how the exam assesses content from the course. With the additional materials covering test taker's responses and scoring keys, teachers...

Give classes a sneak peek at an upcoming test. Scholars work released items from the AP Calculus AB test to prepare for their own exams. The resource consists of six items, two graphing calculator items, and four non-calculator items....

What is the important stuff? The free-response questions from the 2013 Calculus AB exam highlight the topics in calculus assessed that year. Items provide pupils the opportunity to experience questions similar to what they will see on...