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I have a voluntary hand in I am working on, and in that rigard I need to draw the following figure in Maple.

The area $ \displaystyle \iint_R \frac{x}{\sqrt{x^2+y^2}} \mathrm{d}A $ where $R$ is the area where $x>0$ below $3 + \sqrt{9-x^2}$ and above $y=x/3+2$

I have been able to draw the base of the figure in maple (image), but I am not able to draw it in 3d.

The base

I have been able to transform the integral into polar coordinates, but is this easier to draw? Eg

$$\int_{\pi/4}^{\pi/2} \int_{r_2}^{r_1} \cos \theta \, r \, \mathrm{d}r\mathrm{d}\theta$$ Where $y=3+\sqrt{9-x^2} \ \Leftrightarrow \ r_1 = 6 \sin \theta \ $ and $ \ y = x/3 + 2 \ \Leftrightarrow \ r_2 = \cfrac{6}{3\sin\theta - \cos\theta}$

So yeah, any help in drawing this area in maple is greatly appreciated =)

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3 Answers 3

up vote 2 down vote accepted
plot3d(x/sqrt(x^2+y^2), x=0..3, y=x/3+2..3+sqrt(9-x^2),
   axes=box, orientation=[-120,30,0]);

enter image description here

plot3d(x/sqrt(x^2+y^2), x=0..3, y=x/3+2..3+sqrt(9-x^2),
   axes=box, orientation=[-120,30,0], filled=true);

enter image description here

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In Mathematica you could write:

Plot3D[x/Sqrt[x^2 + y^2], {x, 0, 3}, {y, 2, 6}, RegionFunction -> 
       Function[{x, y, z}, x/3 + 2 < y < 3 + Sqrt[9 - x^2]]]

enter image description here

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plot3d(2-x-y, [x,1,2], [y,3,4])$,(filled=true);

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