Why does the area under a curve equal the antiderivative?
The rate of area-accumulation is given by the height of the curve, i.e. the value of the function.
You can see this easily with constant functions: a horizontal line 2 units above the horizontal axis accumulates area underneath at a rate of 2 square units per unit of length.
Why does the area under a curve equal the antiderivative?
The rate of area-accumulation is given by the height of the curve, i.e. the value of the function. You can see this easily with constant functions: a horizontal line 2 units above the horizontal axis accumulates area underneath at a rate of 2 square units per unit of length.
At least that’s how I like to think about it.