MATH 27 Lecture Guide UNIT 3 (IMSP,UPLB) 1 MATH 27 LECTURE GUIDE UNIT 3. APPLICATIONS OF THE DEFINITE INTEGRAL The definite integral has numerous applications especially in the fields of physics, engineering, and probability and statistics. In this unit, we discuss some applications of the definite integral. In particular, we deal with problems involving certain geometric quantities such as the area of a region, the volume and surface area of a solid, the length of an arc, and the center of mass of a region and of a solid. Our goals for this unit are as follows. By the end of the unit, you should be able to solve for the area of a plane region; solve for the volume of the solids of revolution using disk and cylindrical shell methods; identify when to use disk or cylindrical shell method; find centroids of plane area and solids of revolution; find the length of arc of a curve; and solve for the area of surfaces of revolution. Note: It is expected that you already know how to evaluate definite integrals. Most examples and exercise problems will only require setting up the definite integral that will solve for the measure of the object required. In case you forgot, this is how definite integrals are evaluated:RECALL:If ?is continuous on [?,?]and ????=𝑭?+𝑪,then ??????=𝑭?−𝑭?.