Week+20+Jan+26-30

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Monday Jan 26th




Tuesday Jan 27th
During class today we talked about finding the area between a line and a sideways parabola. Building rectangles within the region proved problematic since, in part of the region, the top and bottom of the rectangle was on the same curve. To remedy the situation, "horizontal" rectangles were discussed which changed the variable of integration to y instead of x. This problem is shown in the graphic below.

Wednesday Jan 28th
Today in class we worked with volumes of solids formed by rotating certain areas about the y and x axis. Below are the slides from today.

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Thursday Jan 29th
Today we used the definite integral to determine the volume of a solid using the cross sectional area of the solids as the basis for the solid. Below are the slides and examples from today

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Friday Jan 30th
Finding volumes of solids by slicing is so much more fun when the solid is a delicious, chocolate bundt cake. Before enjoying the cake, however, we had to learn the shell method for finding volumes and this is method is explained on the [|Visual Calculus] website.

We were each given a slice of cake and we first had to model the curved part of the perimeter of our slice using a function of our choosing. Most students used either a quadratic function or a sine function, both of which gave reasonable answers to the volume of the cake.