Find the volume of the solid in the first octant bounded by the coordinate planes, the plane `x=3` , and the parabolic cylinder  `z=4-(y)^2`



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Posted on (Answer #1)

You should first sketch to see how your body looks like. if you want you can use some of the following programms: Matlab, Mathematica, Matcad, or their free alternatives: wolframalpha, octave. 

I can't show you the graph should look like because the graphing tool does not allow 3D graphs.

Now to calculate volume of the solid, you use the following formula:

`V=int int_S f(x,y)dxdy` where `S` is the area under parabolic cylinder and `f(x,y)=z`.

Hence we haave:

`V=int_0^3dx int_0^2 (4-y^2)dy=int_0^3(8-8/3)dx=int_0^3 16/3dx=16`

Hope this helpes

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