Let R be the region bounded by y = 8 sin(2), y = 8(x - 2)², and y = 2z + 6, and containing the point (2,8). a) Find the area of R b) Find the volume of R rotated about the x-axis Find the volume of R rotated about the y-axis d) Suppose R is the base of a shape in which cross-sections perpendicular to the x-axis are squares. Find the volume of this shape.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Let R be the region bounded by y = 8 sin (z), y = 8(x - 2)², and y = 2x + 6, and containing the
point (2,8).
a) Find the area of R
b) Find the volume of R rotated about the x-axis
c) Find the volume of R rotated about the y-axis
d) Suppose R is the base of a shape in which cross-sections perpendicular to the x-axis are squares. Find the
volume of this shape.
Question Hels o
Transcribed Image Text:Let R be the region bounded by y = 8 sin (z), y = 8(x - 2)², and y = 2x + 6, and containing the point (2,8). a) Find the area of R b) Find the volume of R rotated about the x-axis c) Find the volume of R rotated about the y-axis d) Suppose R is the base of a shape in which cross-sections perpendicular to the x-axis are squares. Find the volume of this shape. Question Hels o
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