# Multivariable calculation – How to calculate the area of ​​a function if I am its gradient?

There is a function:

$$f: mathbb {R} ^ {n} rightarrow mathbb {R}, , f ( vec {vb}) in (- infty ,a], a in mathbb {R}, , n> 0$$

and I want to follow the gradient of this function $$nabla (f ( vec {vb}))$$ until I reach the maximum functions. What is the area that I have traveled following in the area? What is the basic calculation behind?

Thank you.