Integrals Teacher Resources
Find Integrals educational ideas and activities
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The Method of Integration by Partial Fractions
In this calculus worksheet, students solve problems using integration by partial fractions. They add fractions to get a common denominator, then take the derivative. There are 20 questions with an answer key.
In this calculus worksheet, students integrate various functions, find the sum of a series, and solve differential equations. There are 16 questions including multiple choice and free response.
Integration of Trigonometric Integrals
In this trigonometry worksheet, students use integration to solve for the six different trigonometric identities. They use indefinite integrals to solve problems. There are 27 questions with an answer key.
In this evaluating integrals worksheet, students solve and complete 30 various types of problems. First, they use the trigonometric identity to rewrite the integrals. Then, students substitute and use integral formulas for sine function.
STEMbite: The Calculus of Building Blocks
Watch this video with your junior engineers or your higher-level mathematicians. In it, Drew builds half of an arch bridge with building blocks. There happens to be a magnetic board behind the blocks, on which he affixes a magnet for each block. When the blocks are removed, what appears to be a graph of an integral function, a natural logarithm, is left behind. Really revealing!
The Ant and The Turntable-Frames of Reference
In this frames of reference worksheet, students solve 5 problems given the details of a journey an ant takes from the center of a CD ROM to its edge. Students draw a scaled sketch of the turntable showing the motion of the ant from different perspectives, they identify the equation for the radial motion of the ant and they evaluate the arc length integral formula to determine the ant's arc length. They also solve an inquiry problem about the ant's path of travel.
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 topics.
Fundamental Theorem of Calculus
High schoolers, with the assistance of their TI-84 Plus / TI-83 Plus calculators, explore and assess the connections between an accumulation function, one defined by a definite integral, and the integrand. They summarize that the derivative of the accumulator is the integrand.
Students approximate the arc length of a cycloid. In this arc length of a cycloid lesson, students solve a problem from an episode of NUMB3RS involving the rotation of a tire. Students take th integral of the the cosine function. Students plot a cycloid as a tire rotates. Students approximate the arc length of a curve by drawing segments spanning the arc.
Parametric, Vector, Polar, and 3D Functions
Twelfth graders investigate the capabilities of the TI-89. In this calculus lesson, 12th graders explore the parametric equation for a circle, for arc length of curves, and for trajectories. Students investigate the symbolic and graphical representation of vectors. Students use polar functions of investigate the area bounded by a curve. Students investigate a 3D graphing application.
Area under curve
Twelfth graders investigate an application of definite integrals. In this Calculus lesson, 12th graders use the symbolic capacity of the TI-89 calculator and the concept of the definite integral to explore the area bounded by a function and the x-axis.
Twelfth graders explore an application of the definite integrals. In this calculus lesson, 12th graders graph three functions on the same domain and each goes through the same three points. Students use the symbolic capacity of their calculator and calculus to find the shortest of each of the paths through these points. Students explore the piece-wise linear function which also goes through the three points.
I'm Lovin' It: Finding Area Between Curves
Students explore the concept of finding the area between two curves. In this finding the area between two curves lesson, students model the logos of McDonalds, Nike, and Motorola on grid paper. Students find functions to represent the logos. Students find the area between two curves of each logo by taking the integrals of the functions.
The Second Fundamental Theorem of Calculus
Students 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.
The First Fundamental Theorem of Calculus
Solve problems using the fundamental theorem. In this calculus lesson plan, students solve problems using theorems and proving theorems. They derive the fundamental theorem as they study it.
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.
Integration By Parts
Pupils solve problems using integration by parts in this calculus lesson plan. Learners apply the product rule and integration by parts. They graph the equation and use the TI to observe the integration process.
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.
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.
Elevator Height as Integral of Velocity
Pupils investigate integrals and their relationship to velocity in this calculus lesson. They use the idea of a moving elevator to explore vertical motion and use the TI to help them create a visual.