Approximate
Volumes under a Surface using the Riemann Sum
Example: Estimate the volume of a solid S that lies below
the surface, f(x,y) = 2xy and above the rectangle {(x,y), | 0 ≤ x ≤
3, 0 ≤
y ≤ 2 } a. Use a Riemann sum with m = 3 and n = 2 and
take the sample point to be the upper right corner of each rectangle. b. Use the midpoint rule to estimate the
volume of the solid as in part a. |
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Strategy: First show the rectangular
grid and sample points for part a. |
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Next set up table to calculate
the double Riemann Sum for part a.
∑ of
individual volumes = total volume = 36
result |
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Click here to continue
with part b of this example. |
Copyright © 2018 Richard C. Coddington
All rights reserved.