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Suppose that 'a' is a positive constant and that 'R' is the region bounded above by
y = 1/xa,
below by y = 0, and on the left by the line x = 1.
a) Sketch the curves
y = 1/xa
for a = .5, 1 and 2. Which of these is closest to the x-axis?
b) For which positive numbers 'a' (now considering all positive numbers) do you get a convergent integral when you attempt to calculate the area of 'R'?
c) Same as b), but for the volume of the solid obtained by rotating 'R' around the x-axis.
d) Same as c), but for the volume of the solid obtained by rotating 'R' around the y-axis.
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