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Integrals Teacher Resources
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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!
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 activity, 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.
In this Calculus worksheet, students assess their understanding of various topics, including the derivatives of trigonometric functions, evaluating integrals, sigma notation, and convergent and divergent series. The one page interactive worksheet contains fifty-two problems. Answers are not provided.
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.
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.
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.