a) ††††††††††††††††† b) †††††††††††††††††† c) †††††††††††††††††††††††† †d)†††††††††† ††††††††††† e)
a) Find the volume of the resulting solid.
b) Use the part a) to find the of the centroid of the region R (hint: theorem of Pappus). You may use the fact that
a) Find such that the error bound for Simpsonís rule is less than or equal to the error bound for the midpoint rule.
b) Does this necessarily mean that Simpsonís rule is better than the midpoint rule for this choice of ? (Why or why not?)
c) How small should the length of the interval [a,b] be so that Simpsonís rule with †has a smaller error bound than the midpoint rule for ?
a) Find the length of this curve from to
b) What is the surface area obtained when this curve from to †is revolved about the ?
a) Use any method that you wish to find the centroid of the region (besides quoting a formula).
b) Use part a) to find the volume obtained when the region is revolved about the line