How do I write an expression like this question in matlab codes and execute it without errors but logical answers?

Using double integral.Find the volume of the solid lying under the elliptic paraboloid x2/4+y2/9+ z = 1 and above the rectangle R = [−1,1]×[−2,2]

[KSSV]

Any of our attempts?

[Eneriko Ratuloaloa]

trying, but it is not in matlab coding except mathematical expression. Trying to input it as a matlab coding

[madhan ravi]

Z coordinate of the rectangle because the domain not fully defined.

[Eneriko Ratuloaloa]

do you have any clue on converting a maple coded expression into matlab coding, coz I got a maple expression for the problem, solved.

[Eneriko Ratuloaloa]

with(plots); f := (x,y) ->1-x^2/4-y^2/9: a := -1: b := 1: c := -2: d := 2: pic1 := plot3d(f(x,y), x = a ..b, y = c..d, color=red, style=patch): pic2 := plot3d( [x, c, f(x,c)*u], x = a..b, u = 0..1, color=yellow): pic3 := plot3d( [x, d, f(x,d)*u], x = a..b, u = 0..1, color=yellow): pic4 := plot3d( [a, y, f(a,y)*u], y = c..d, u = 0..1, color=yellow): pic5 := plot3d( [b, y, f(b,y)*u], y = c..d, u = 0..1, color=yellow):

display3d({pic1, pic2,pic3, pic4,pic5}, axes=framed; orientation = [45,80]; title = `f := (x,y) ->1-x^2/4-y^2/9`, titlefont = [HELVETICA, BOLD, 10]); int( int( f(x,y), x=-1..1), y=-2..2); 166/27;

if true
  % code
end

[madhan ravi]

select the whole code and press the code button{} so that its easier to read

Answer 1

[Dimitris Kalogiros]

Try the following script

close all
clearvars

syms x y z

z=-(x^2)/4 - (y^2)/9 +1

fsurf(z); 
xlabel('x'); ylabel('y'); zlabel('z');

vol= int( int(z, x, -1, 1  ) , y, -2, 2)

If you run it, it would give something like this:

[Eneriko Ratuloaloa]

Thanks mate, I did manage to solve the issue.

Answer 2

[satish]

find the volume of the solid S that is bounded by the elliptic paraboloid x^2+2*y^2+z-16=0, the planes x=2 and y=2 and the three coordinate planes.

[Walter Roberson]

please expand on the mathematics to demonstrate that this volume is the same as the volume that the original poster was asking about. The identity of those two volumes is not obvious to me, so I do not understand how this is a solution to the question asked.