INTEGRATION BY SUMMATION

PROBLEM

A thin plate is in the shape of the region above the parabola and below y=x. Assuming that the density at (x,y) is .

1. Express the mass of this plate as an iterated integral using vertical strips and obtain its numerical value.
2. Subdivide the plate into small squares of width h using lines parallel to the x and y axes. Using this subdivision approximate the mass of this plate. Please state the final formula clearly and show all the intermediate steps.
3. Using Maple obtain the value of this approximation for . I suggest you introduce intermediate functions to break complicated formulas into more managable parts.

 
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