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Mean Value Theorem to calculate solids of revolution?
Ive been studying calculus on my own because my school doesn't offer it and i came across solids of revolution tonight. In one of the problems it says "What is the volume of the solid formed by rotating y=e^x across the x-axis between x=2 and x=3 ?" They did it using the disk method. It occurred to me however, that if you used the mean value theorem to find the average height of the curve, that would give you the average radius, so then u should just be able to use (pi)(r^2)(height) to find the volume, but height is just 3-2=1 . But it always seems to come up short. Does anybody know why?
Ive been studying calculus on my own because my school doesn't offer it and i came across solids of revolution tonight. In one of the problems it says "What is the volume of the solid formed by rotating y=e^x across the x-axis between x=2 and x=3 ?" They did it using the disk method. It occurred to me however, that if you used the mean value theorem to find the average height of the curve, that would give you the average radius, so then u should just be able to use (pi)(r^2)(height) to find the volume, but height is just 3-2=1 . But it always seems to come up short. Does anybody know why?
