How can you integrate a three variable functions?

Answer 1

Assuming you are integrating with respect to one of the three variables, you integrate normally. For example:

∫(x+y+z)dx

= ∫ x dx + ∫ y dx + ∫ z dx (Integral of the sum is the sum of the integrals)

= x^2/x + yx + zx + C

Or a harder one:

∫ (sin^2(y)+sqrt(z))/x dx

= (sin^2(y) + sqrt(z))*∫ 1/x dx (Factor out constants)

= ln(x)*(sin^2(y) + sqrt(z))

tl;dr: just do it normally with normal integration rules

Answer 2

To integrate a three-variable function, you need to perform a triple integral. This involves integrating the function with respect to each variable individually, in the order specified by the given problem. The result will be a scalar value representing the integral of the three-variable function over the specified region.