Multivariable Calculus with Mathematica

Copyright: Kevin Coombes, Paul Green, and Ronald Lipsman, 1998.

Multiple Integrals -- the 2D Case
Quiz

Immediately Type Your Name
Here:
Type your Loginid Here:

Solve the following question in this Notebook. 

When you are done, save the Notebook in the Homework folder under the name
	loginname-quiz08.nb
For example, if your login name is RLL00, you click on 
File:Save As..., navigate to the folder ``Homework'' , and use the file name ``RL00-quiz08.nb''

Warning!! You will only be able to save this Notebook ONCE in the Homework folder. If you wish to do interim saves, use your own directory. Only the Notebook in the Homework folder will be graded.

Compute the following double integral∫(∫_R) h(x,  y) dA. Visualize the region of integration:

 h  =  (Sqrt[x  +  y]);  
R = the bounded region in the first quadrant between the curves  1  - (x^3)  +  3  (x^2)  - 2  x and (e^(-(x^2))).

In case you misplaced it, here is the visualization program:

\(verticalRegion[a_, \ b_, \ f_, \ g_]\  := \ 
      Module[{twocurves}, 
	
        twocurves\  = \ 
          Plot[{f, \ g}, \ {x, \ a, \ b}, \ 
            PlotStyle\  -> \ {{}, \ Thickness[0.008]}, 
            DisplayFunction -> Identity]; 
	
        Show[twocurves, \ 
          Table[Graphics[Line[{{x, \ f}, \ {x, \ g}}]], 
            \ {x, \ a, \ b, \ \((b - a)\)/20}], 
          DisplayFunction -> $DisplayFunction]]\)