Integration of Functions of Two Variables

In this lesson, the integration of functions of several variables will be addressed. It plays a very important role in any problem of physical interest. The first step consists in a one-dimensional integration of a function of two variables. Given a function \(f: \mathbb {R}^2 \rightarrow \mathbb {R}\) partially differentiable with continuous first derivatives, the new function defined by means of the integral: \( \int _{\alpha (x)}^{\beta (x)} dy \, f(x,y) =: F(x)\) is here considered.