Find volume by the cylinder method.
The functions y=18x-3x² and y=9x intersect at x=0 and x=3 to form an enclosed area.
The area of a slice of thickness dx at x has a height of 18x-3x²-9x, and an incremental area of dA=(18x-3x²-9x)dx.
Rotate this incremental area about the y axis to get a cylinder of volume:
dV=2πx(18x-3x²-9x)dx
Integrate from x=0 to x=3 give the volume of rotation
∫dV [x=0 to x=3]
=∫2πx(18x-3x²-9x)dx
=[3(π(4x^3-x^4))/2 for x=0 to 3
= 81π/2.
The answer is even close to any of the given answers. So please check for typo in the question, or an arithmetic error in my calculations.
Find the volume generated by revolving the region bounded by y=18x-3x^2 and y=9x about the y-axis.
a. pi/12 b. pi/6 c. 3pi/4 d. pi/3
help! .. :D
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