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4/30/2015 Perkins AP Calculus AB Day 4 Section 7.2

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How do you find the volume of the figure formed by revolving the shaded area about the x-axis? Revolving this function creates a solid whose volume is larger than we want. Revolving this function carves out the part we don’t want. Outside radius Inside radius The volume we want is the difference between the two.

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Washer Method (for finding the volume of a solid of revolution) Outside radius Inside radius

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1.Find the volume of the solid generated by revolving the area enclosed by the two functions about the x- axis. Find intersection points first. Washer Method:

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2.Find the volume of the solid formed by revolving the area enclosed by the given functions about the y- axis. This region is not always created by the same two functions. The change occurs at y = 1. We need to use two integrals to find the volume. Since we’re revolving about the y-axis, each radius must be in terms of y. (distance from the parabola to the x-axis) (distance from the parabola to the y-axis) For y in [0,1] we use disk method. For y in [1,2] we use washer method.

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Perkins AP Calculus AB Day 4 Section 7.2

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How do you find the volume of the figure formed by revolving the shaded area about the x-axis?

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Washer Method (for finding the volume of a solid of revolution)

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1.Find the volume of the solid generated by revolving the area enclosed by the two functions about the x- axis.

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2.Find the volume of the solid formed by revolving the area enclosed by the given functions about the y- axis.

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