Question

When using integration to find an area, exactly which "area" is found?

Answer 1

If we consider the general integral:

`I = int_a^b \ f(x) \ dx`

Then the Integration calculates the "net" area between the curve `y=f(x)` from `x=a` to `x=b`, and the `x`-axis.

By "net" area, we consider any area below the curve and above the `x`-axis to be positive , and any area above the curve and below the `x`-axis to be negative.