Multivariable Calculus with Mathematica
Copyright: Kevin Coombes, Paul Green, and Ronald Lipsman, 1998.
Multiple Integrals -- the 2D Case
Quiz
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Solve the following question in this Notebook.
When
you are done, save the Notebook in the Homework folder under the name
loginname-quiz08.nb
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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:![[Graphics:multintquizgr1.gif]](multintquizgr1.gif)
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 Exp[-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]]