"To compute the area under a curve. We need to take every point where the function is defined and sum up all the tiny line we obtain. This is ∫baf(x)dx
We are summing up tiny rectangles of height f(x) and width dx. But because there are infintely many points in the interval [a,b] and because a point has no width, we can't sum up all of them or we will obtain of result of [infinity]. That's why we sum up with a width of dx. But by doing that we are not really precise on the computation, this is not the smallest measurment possible, we have a roundness error right ?
