AppIntegday3notes

# AppIntegday3notes - Applications of Integration Day 3...

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Calculus Applications of Integration Page 9 Applications of Integration Day 3 Volumes of Solids by Plane Slices Consider the volume of a cylinder Consider a bounded region and rotating that region around the x-axis. Take a slice and consider its volume. Take the sum of the volumes of each slice. What do you get? Volume formula:

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Calculus Applications of Integration Page 10 Example 1 The region bounded by the curve y = x and the x-axis over the interval [1,4] is rotated about the x-axis to generate a solid. Find the volume of the solid. Find the volume of the solid generated by revolving the region bounded by the lines and curves about the x-axis Example 3 Example 4 y = x 2 , x = 2, y = 0 y = sec x , x = π 4 , x = π 3 , y = 0
11 Find the volume of the solid generated by revolving the region bounded by the lines and curves about the y-axis Example 5 Example 6 y = 1 x 2 , y = 0, x = 0 x = 3 y 2 , y = − 1, y = 1, x = 0 Example 7 The region bounded by the curve

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AppIntegday3notes - Applications of Integration Day 3...

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