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Lecture

6.3 Volumes by Cylindrical Shells Question #3 (Medium)

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Department
Mathematics
Course
MAT136H1
Professor
all
Semester
Winter

Description
6.3 Integral Applications Cylindrical Shells Question #3 (Medium): Finding Volume by Cylindrical Shells Strategy First, graph the region bound by the function and the lines. If the rotation is not typical or -axis, then measure from the line of rotation and modify the radius accordingly. If the height stretches vertically and the interval for integral moves across horizontally, the rotation is about the -axis. Similarly, if the height lies horizontally and the interval for integral moves up vertically, the rotation is about the -axis. Substitute the appropriately expressed height and the radius into the integral using cylindrical shells to calculate the volume: ∫ . Sample Problem Using cylindrical shells find the volume obtain
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