if mathematically derivatives are the opposite of integrals, conceptually how is the area under a curve opposite to the slope of a tangent line?

Question

if mathematically derivatives are the opposite of integrals, conceptually how is the area under a curve opposite to the slope of a tangent line?

In: 332

Answer 1

It’s more that it’s the opposite treatment. You start with a line…removing a dimension (derivation) transforms that line into a single point. Adding a dimension (integration) transforms the line into a rectangle.

You can find equations that make it not quite a rectangle, but the idea is the same.