The definite integral

The differential $df = f'(x)\,dx$ measures the infinitesimal change of a function. The integral is the inverse operation: an infinite sum of differentials. In this section we define the definite integral as a sum of infinitely many infinitesimal rectangles — that is, as the area under a curve — and set up the model problem that we will solve with the antiderivative.

• The definite integral as a sum of differentials
• The area under a curve