# Thread: a matter of interpretation

1. ## a matter of interpretation

Hi folks,

Nearly all text books on mathematics will tell you that differentiation and integration can be interpreted geometrically. Differentiation is the process of finding the tangent to a curve and integration the area under the curve. We are also told that these are opposite functions and it is plain that they are. I can see that differentiation finds the tangent and that intergration calculates the area but I don't see how one process is the opposite of the other geometrically. How is an area the opposite of a tangent? So my question is: am I overworking the metaphor? Should I stick to just looking at differentiation as a tangent and integration as an area and not expect to see a geometric reason why one process is the reverse of the other?

best regards