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## Chapter 3 The Integral

### 3.1 Introduction

Integration can be thought of as a sum of an infinite number of objects or sections that are infinitesimally small. The integral can be used to calculate area under a curve, area of a region or surface, volume of an object, average value of a function, work done, pressure, as well as the change in a function when its rate of change is known. The last example uses the Fundamental Theorem of Calculus.

• Just as the derivative can be thought of as the limit of differences, the integral can be thought of as the limit of sums. On the graph of a function, the derivative can be represented by slope of the curve and the integral can be represented by area under the curve. The derivative of distance x is velocity ...

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