Integrals Teacher Resources

Find Integrals educational ideas and activities

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Students explore the concept of average value of a function.  In this average value of a function instructional activity, students use their Ti-Nspire to determine the average value of a quadratic function.  Students take the integrals of velocity functions using trapezoids.
Students explore the concept of arc length.  In this arc length lesson, students find the arc length of a sine curve over a specific interval using integrals.  Students use their Ti-Nspire to determine the integrals of sine curves.
In this calculus activity, students use integration to solve word problems they differentiate between integration and anti derivatives, and between definite and indefinite integrals. There are 3 questions with an answer key.
Twelfth graders explore differential equations.  For this calculus lesson, 12th graders explore Euler’s Methods of solving differential equations.  Students use the symbolic capacity of the TI-89 to compare Euler’s Method of numeric solutions to a graphical solution. 
Eleventh and twelfth graders find the volume of figures using cross sections. They use their Ti-Nspire to find the volume of a solid formed by cross sections of a function. Pupils find the integrals of the shapes using cross sections. 
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.
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. 
Twelfth graders explore an application of the definite integrals.  In this calculus instructional activity, 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. 
Twelfth graders investigate an application of definite integrals.  In this Calculus lesson plan, 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. 
Sal continues his discussion of decay by showing students the math involved in determining how much a substance is left after one half-life, two half-lives, and even three half-lives have gone by. He sets up a general function of time that can be used to determine the remaining amount of a substance after 10 minutes, or three billion years have elapsed!
Students explore Riemann Sums.  In this Calculus lesson, students investigate Riemann Sums as an approximation of the value of the definite integral.
Twelfth graders investigate differential equations.  In this calculus lesson, 12th graders are presented with a step-by-step illustrated review of the process used in solving differential equations and an application problem.  Students solve differential equations and application of differential equations. 
Twelfth graders explore integral calculus.  In this calculus activity, 12th graders explore the volume and surface area of an ellipse in the context of an Easter egg problem. 
Twelfth graders investigate convergence of an infinite series.  In this Calculus lesson, 12th graders apply the integral test to determine convergence of an infinite series. 
Twelfth graders investigate an application of definite integrals.  In this calculus lesson, 12th graders explore the use of definite integral to represent the area bounded by two curves.  Students rely on the symbolic capacity of the TI-89 to assist them in solving the problem.
In this Calculus worksheet, students use the TI-89 calculator to compute derivatives and anti-derivatives in order to solve a crossword puzzle. The two page worksheet contains twenty-one problems. Answers are not provided. 
In this calculus worksheet, students integrate given functions following the integration rules. They simplify their answers with trig. values. There are 8 questions with an answer key.
In this college level Calculus worksheet, students evaluate indefinite and definite integrals. The two page worksheet contains ten problems. Answers are not provided. 
In this college level calculus activity, students evaluate the given integrals using integration by parts.    The one page activity contains six problems.  Answers are not provided. 
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! 

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