6.2 Integral Applications
Question #4 (Medium): Volume Approximation Using the Midpoint Rule
When a dataset is given, the volume can be approximated by:
Usually, the number of disks is fixed to be a reasonable value of . So then disappears, leaving only
the summation sign. Thus, ∑
The sample point can be chosen as any point. But the question usually specifies which point to use.
Most common choice is midpoint. The height of individual disk depends on , so , over the
Trunk of a giant tree is in height. It is sliced into thickness to be used as tabletops.
The surface area of each sliced trunk is given in the table.
Use the Midpoint Rule with to estimate the entire volume of the trunk of the tree.
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Midpoint Rule with