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ResourceSpotlight
In this activity, students will be introduced to the concept of finding the volume of a solid formed by cross sections of a function that form certain shapes. Since volume is the area of the base times the height and dV = Area dx, student review areas of various shapes like squares, semicircles, and equilateral triangles. Geometry Trace is used to help students get a “3D” visual of the volume under consideration.
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Texas Instruments, Inc.
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ResourceSpotlight
Students are asked some exam-like multiple-choice questions to introduce separable differential equations. Students will use the "deSolve" command to find general and particular solutions to differential equations. They will also dynamically explore the family of particular solution to a differential equation.
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Texas Instruments, Inc.
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ResourceSpotlight
Students are introduced to the important topic of simple harmonic motion in terms of the motion on a swing. Using multiple representations to support understanding, students derive the defining formulas first, beginning with the trigonometric relationship between time and displacement, and differentiation to the form for acceleration, and then by integration from acceleration back to displacement. This activity provides an introduction to differential equations.
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Texas Instruments, Inc.
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ResourceSpotlight
Students will investigate the arc length of the Gateway Arch. They will use the Pythagorean Theorem to approximate and use Calculus to find the exact solution. They will also use CAS capabilities (including the arcLen command), to solve a variety of arc length questions.
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Texas Instruments, Inc.
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An overview of integration techniques to determine volume. It includes examples on ring/washer method, cylindrical shells, volumes by cross-sections.
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Paul's Online Math Notes
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A helpful scientific calculator that runs in your web browser window.
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Holt Online Learning
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In this video, Salman Khan of Khan Academy explains the Laplace transform. Part 2 of 6.
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Khan Academy
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This calculus integral reference sheet contains the definition of an integral and the following methods for approximating definite integrals: left hand rectangle, right hand rectangle, midpoint rule, trapezoid rule, and Simpson’s rule. There is a list of many common integrals. Also included in this reference sheet is nice table for trigonometric substation when using integrals. Integration by substitution is defined as well as the integration by parts.
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eCacl.com
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Good pictures showing the volume of revolution.
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calstate education
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Very extensive help sheet that contains everything from simple derivative/integration formulas, to quick explanations of advanced derivation and integration techniques.
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Pauls Online Math Notes
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