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Find the volume of the solid bounded by the surface z= 5+(x-y)^2+2y and the planes x...

Find the volume of the solid bounded by the surface z= 5+(x-y)^2+2y and the planes x = 3, y = 3 and coordinate planes.

a. First, find the volume by actual calculation.  

b. Estimate the volume by dividing the region into nine equal squares and evaluating the functional value at the mid-point of the respective squares and multiplying with the area and summing it. Find the error from step a.  

c. Then estimate the volume by dividing each sub-square above into 4 sub-squares and follow the process/steps in (b) above. Find the error from step a.

d. Keep repeating step b to a reasonable number to minimize the errors from step a.

Math   Advanced-Math   
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