How to find surface area ?

how can I find a surface area of this function on certain interval.

f = @(x,y,z) cos(x) + cos(y) + cos(z);

Answer 1

[Walter Roberson]

https://courses.lumenlearning.com/suny-openstax-calculus1/chapter/arc-length-of-a-curve-and-surface-area/

So probably something close to

f = @(x,y,z) cos(x) + cos(y) + cos(z);
syms x y z real
syms xl xh yl yh zl zh real
F = f(x,y,z);
SA = int(int(int( sqrt( 1 + diff(F,x).^2 + diff(F,y).^2 + diff(F,z).^2), z, zl, zh), y, yl, yh), x, xl, xh);
disp( char(simplify(SA)) )

int(int((ellipticE(zh, 1/(cos(x)^2 + cos(y)^2 - 3)) - ellipticE(zl, 1/(cos(x)^2 + cos(y)^2 - 3)))*(3 - cos(y)^2 - cos(x)^2)^(1/2), y, yl, yh), x, xl, xh)

[Teerapong Poltue]

it isn't work.

I couldn't get from a certain interval as I expected.

[Walter Roberson]

you would substitute your interval bounds for xl xh yl yh or zl zh

Note that there probably is no closed form so you might need to vpa()