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2b. Set up (but do not evaluate) an integral for the volume of the solid formed by revolving the region from #1 about the y-axis
3. Find the average value of on the interval [0,3].
4. Set up (but do not evaluate) an integral to determine the arclength of on [0,3].
5. The demand function for ACME Widgets is , where p is measured in dollars and x is the number of widgets sold monthly.
Suppose ACME wants to sell 1000 widgets each month:
a. What is the price that ACME should charge?
p(1000) = , so $5 each.
b. What is the consumer surplus when the price is set at this level?
Area of cross-section for a slice at height x:
Volume of this slice:
Mass of this slice:
Weight of this slice:
Distance to lift this slice from its starting height of x to the top: (10-x) meters
Work required to lift this slice:
Total work required:
Integrate this to get the answer.
7. The plate shown is bounded above by. Find the coordinates of its center of mass.
By symmetry (or formula), the x coordinate of the center of mass must be 0.
The y coordinate is