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

Let’s say you have the derivative of a function. So, you know how the function varies.

In order for you to know the original function, you just need to integrate the derivative that is, add up little pieces that make the derivative, since they together “make” the original function

So, for instance, if you have a derivative and break it down into discrete intervals of 3 5 2 -1, that means it grew 3, then 5, then 2, then shrinked one. By integrating, you’ll add up all the area under the curve, so the cumulative effect of each variation, and get an original function of 0 3 8 10 9 (assuming you’re starting at 0).