Section 7.1 Areas
Our study of integrals was motivated by the area problem so it feels necessary to at least note that in a fairly broad sense, we’ve solved the area problem. Consider, for example, and Let’s graph them both together.
Take a look at that oddly shaped area trapped between the two curves. Can we calculate that area? Sure. We have the skills now. Notice that the area occurs over the interval The curve on top is
An antiderivative of is so that according to the FTC, the area under that curve is The curve on the bottom is
An antiderivative of is so that according to the FTC, the area under that curve is So, the area trapped between is -- very quick to calculutate with the skills we now have.