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