Solid that lies above the square (in the xy-plane)

[Whatupdoc]

Consider the solid that lies above the square (in the xy-plane) R= [0,1] X [01]
and below the elliptic paraboloid z= 64 -x^2 +4xy -4y^2

Estimate the volume by dividing R into 9 equal squares and choosing the sample points to lie in the midpoints of each square.


i'm not sure how you would dividing R into equal squares, cause it's an odd number. can someone help me get this started

 

[Tide]

That would be a 3X3 array of squares which is reasonable considering that the paraboloid is off-center with respect to the square. Obviously, if you divided the original square into a much larger number of areas you would get more accuracy at the expense of doing a lot more work. Fewer squares mean less work but also reduced accuracy. 9 seems like a good optimum!

 

[Whatupdoc]

i don't know what i was thinking, thank you