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

A simple example of this is with two basic physics functions—velocity and distance. Velocity being the derivative of distance, indicates the slope of that function, or the rate the distance changes with time. The integral of all of those rate changes ends up being the sum of all of the instantaneous velocity values over the course of a time period, to indicate the distance, or area under the velocity curve.

The relationships are easier to conceptualize looking at Riemann sums too