West Contra Costa Unified School District
Indefinite Integrals
The inverse of matter is anti-matter, so the inverse of a derivative is an antiderivative. The instructional activity introduces antiderivatives and indefinite integrals to the class along with the notation for integrals. Groups work...
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Integration by Substitution
Looking for help in introducing integration by substitution to your calculus students? Here is a lesson that walks a learner through a review of the change rule, and then by starting with more recognizable derivatives, it helps them...
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Computing Indefinite Integrals
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...
Shodor Education Foundation
InteGreat
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 midpoint...
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Evaluating Definite Integrals with Substitution
Students evaluate and define limits using substitution. For this calculus lesson, students apply the use of Integrals to explore Newton's law of Cooling. They solve rate and temperature problems using Integrals.
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Definite Integral
Learners investigate the intervals represented by a function in this calculus lesson. They decide what interval of the function will be positive, negative or zero. They are then given graphs of functions and asked to analyze it.
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The Fundamental Theorem of Calculus and Properties of the Definite Integral
Students discuss the importance of fundamental theorems in math. In this calculus activity, students define the fundamental theorem of calculus and discuss why it is so important they understand it. They work problems to model how this...
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Integration by Parts
Students explore integration by parts and use it to solve equations. In this calculus instructional activity, students sing a song about integration, and practice solving equations using integration by parts twice. They solve integrals...
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AP Calculus Exam Prep
Pupils practice sample questions from the AP Calculus Exam. They solve calculus problems involving bounded regions, integration, derivatives, and limits. They then answer free response and multiple choice questions on the above mentioned...
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The Second Fundamental Theorem of Calculus
Learners investigate the fundamental theorem of calculus. In this calculus instructional activity, students derive the fundamental theorem of calculus. They differentiate between the first and second theorem.
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Integration By Substitution
Young scholars calculate the solution using integrals in this calculus lesson. They use the TI to create a visual of how to compute integrals. Learners also use substitution by integration and all its properties.
Texas Instruments
Integration By Parts
Pupils solve problems using integration by parts in this calculus lesson. Learners apply the product rule and integration by parts. They graph the equation and use the TI to observe the integration process.
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Piecewise Linear Integral
Young mathematicians solve and graph piecewise functions in this calculus lesson. They integrate linear functions containing restrictions and graph their answers using the TI.
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The First Fundamental Theorem of Calculus
Solve problems using the fundamental theorem. For this calculus lesson, high schoolers solve problems using theorems and proving theorems. They derive the fundamental theorem as they study it.
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Integration By Parts and Quiz on Basic Integration Formulas
Students solve integrals using integration by parts. In this calculus lesson, students review problems using integration by parts, repeated integration by parts and constant integration. They take a Quiz after they solve review problems.
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Integrals with even Powers of Sine and Cosine
Twelfth graders define integrals and solve equations with trig functions. In this calculus lesson, 12th graders integrate integrals with sine and cosine powers. They discuss what method to use based on even or odd exponents.
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Integrals involving Trig Substitution
Students define integrals and list the trig values. In this calculus activity, students integrate functions using trig substitution. They solve integrals containing sums and differences of squares.
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Integration Involving Inverse Trig Functions
Students review the steps for integration and solve equations using integration by parts. In this calculus lesson, students apply their knowledge of integration to inverse trig function. Students review their trig and inverse trig...
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Elevator Height as Integral of Velocity
Pupils investigate integrals and their relationship to velocity in this calculus instructional activity. They use the idea of a moving elevator to explore vertical motion and use the TI to help them create a visual.
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Integration By Parts
Twelfth graders define integration by parts and solve integrals. In this calculus lesson, 12th graders integrate functions using the product rule. They work example problems with the teacher before doing it on their own.
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Integrals by Partial Fractions
Young scholars solve integrals using partial fractions. In this calculus instructional activity, students solve equations using the Heaviside Method if all the number in the denominators are not repeating. They complete an assignment in...
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Numerical Methods of Integration
Students calculate the area under a curve. In this calculus lesson, students estimate and calculate the area of a curve using simpson's rule and the trapazoidal rule. They review rieman sums and add to it.
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Integrals with odd powers of secant and tangent
Twelfth graders solve equations containing powers of sec and tan. In this caclculus instructional activity, 12th graders integrate integrals that have odd powers of trig functions. They use trig substitution to solve these problems.
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Integrals involving Trig Substitution
Twelfth graders solve derivatives using trig substitution. For this trigonometry lesson, 12th graders integrate integrals by substituting trig values into the equations. They review detailed examples before solving problems on their own.