Area under the Curve

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We discuss how to approximate the area under a curve.

We turn now to a seemingly totally unrelated topic; areas of shapes. We have a number of formulas for relatively nice geometric shapes, like rectangles, triangles, and many regular polygons. But what about an arbitrary shape formed by a curve? In this section we aim to give an intuitive argument on how we can approximate the area of a shape formed by a function’s graph and the x-axis, the so called “area under the curve.”

Video Lecture

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So we’ve seen that we can get approximations for the area under the curve by using rectangles spread throughout the region and using the easy-to-calculate sum of the area of those rectangles. We will get to the analytic process to do this in another segment, but the geometric intuition will be useful as we investigate various analytic approaches to find the area.