I am confused: definite and indefinite

摘要： Indefinite integral and definite integral.Think of a metaphor:the x values are time points...

Indefinite integral and definite integral.

Think of a metaphor:

the x values are time points.

The y values are distance.

The gradients are speed.

What you are trying to find is the distance runned from one time point to the other, in other words, the distance changed, which is the change in y values. In calculus, this is dy. You are given the 导数, a formula that tells you a pattern in which the speed changes. In definite integral, you are also given two time points. In calculus, what you are going to find is the change of y value between two x values, given how the gradient changes. In indefinite integral, you know how the gradient changes, how the speed changes. From this, you can find what the speed is at every time point, but you don't know what the distance changed is.