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Midpoint & trapezoidal sums

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Problem

Approximate the area between the x-axis and f(x)=(x3)2 from x=0 to x=6 using a midpoint Riemann sum with 3 equal subdivisions.
The approximate area is
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
Here's a sketch to help you visualize the area:
A shaded region bounded by the graph of the function f of x equals the quantity x minus 3, squared, the x-axis, the equation x equals 0, and the equation x equals 6.
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