Let R be the region bounded by
y=2sin(2πx),
y=2(x−2)2, and
y=x+1, and containing the point (2,2).
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.
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Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity