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Lecture

# 6.3 Volumes by Cylindrical Shells Question #2 (Easy)

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School
University of Toronto St. George
Department
Mathematics
Course
MAT136H1
Professor
all
Semester
Winter

Description
6.3 Integral Applications Cylindrical Shells Question #2 (Medium): Volume by Cylindrical Shells Rotated About the X-Axis Strategy First helpful step is to graph the given function and lines. Recalling the volume calculation using cylindrical shells: ∫ Given function defines the interval[ ]for integral and which curve denotes the of the cylindrical shells. If this function is given in the form of , when the rotation is about the -axis, then rearrange the function to get the inverse . Then the volume is written as: ∫ . If the function describing the height is given in the form of , no rearrangement is necessary, and so it can be used directly for the integral. Sample Problem Using cylindrical shells find the volume obtained by rotating the region bound by the curves about the - axis. √ , , Solution By graphing the function and the lines, i
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