Problem #34
Michael Booth
15.2
Long

p1=Plot3D[(E^(-(x^2)))*Cos[(x^2)+(y^2)],{x,-1,1},{y,-1,1}]

p2=Plot3D[2-(x^2)-(y^2),{x,-1,1},{y,-1,1}]

f[x_,y_]:=(E^(-(x^2)))*Cos[(x^2)+(y^2)]

g[x_,y_]:=2-(x^2)-(y^2)

plot1==f[x,y]

plot2==g[x,y]

Show[p1,p2,PlotRange->{-1,3}]

I1=Integrate[(E^(-(x^2)))*Cos[(x^2)+(y^2)],{x,-1.0,1},{y,-1,1}]

I2=Integrate[2-(x^2)-(y^2),{x,-1,1},{y,-1,1}]

I would think that I’d find the volume under p1 and subtract the volume under p2. Mathematica isn’t giving me a real number for the volume underneath p1. I’m unsure of what I should do from here.

I2-I1