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.