Students often have a difficult time visualizing the solids of revolution and how the volume and the integral are related. Visualizing Solids of Revolution – Disk Method The shape of the urn determines the characteristics of this graph.Ĥ. The associated graph represents the height of liquid in the urn as a function of the amount of liquid in the urn. The physical context is the filling of an urn with liquid, depicted in a window on the left side of the illustration. The Filling_the_Urn.tns TI-Nspire document provides for a graphical investigation of related rates. This lesson uses a graphical representation of the Mean Value Theorem (MVT) to demonstrate how the theorem relates information about the average rate of change of a function to an instantaneous rate of change. You can view and download the full TI-Nspire activity on our website. This is perhaps one of the quickest ways to visualize Riemann sums and students can look at the left hand, right hand, and midpoint Riemann sums easily for many different functions and intervals.įor more information, download the Teacher Notes (PDF). In this activity, your students can quickly learn that for a continuous nonnegative function f, there is one interpretation of the definite integral f(x)dx from a to b, the area of the region R, bounded above by the graph of y = f(x), below by the x-axis, and by the lines x = a and x = b. These 5 lessons are some of our favorites for helping students to make connections in calculus. Being able to manipulate and see changes in relations can help to solidify concepts and relationships among them. Dynamic visualization is a good tool for helping students to visualize and interact with the mathematics. Often, students have a hard time grasping the concepts of calculus, and even more, making connections among them. Calculus is the study of rates of change and of lengths, areas and volumes.
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