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- https://math.libretexts.org/Courses/Mission_College/Math_3B%3A_Calculus_2_(Sklar)/05%3A_Integration/5.00%3A_Prelude_to_IntegrationDetermining distance from velocity is just one of many applications of integration. In fact, integrals are used in a wide variety of mechanical and physical applications. In this chapter, we first int...Determining distance from velocity is just one of many applications of integration. In fact, integrals are used in a wide variety of mechanical and physical applications. In this chapter, we first introduce the theory behind integration and use integrals to calculate areas. From there, we develop the Fundamental Theorem of Calculus, which relates differentiation and integration. We then study some basic integration techniques and briefly examine some applications.
- https://math.libretexts.org/Courses/Mission_College/Math_3B%3A_Calculus_II_(Reed)/05%3A_Integration/5.00%3A_Prelude_to_IntegrationDetermining distance from velocity is just one of many applications of integration. In fact, integrals are used in a wide variety of mechanical and physical applications. In this chapter, we first int...Determining distance from velocity is just one of many applications of integration. In fact, integrals are used in a wide variety of mechanical and physical applications. In this chapter, we first introduce the theory behind integration and use integrals to calculate areas. From there, we develop the Fundamental Theorem of Calculus, which relates differentiation and integration. We then study some basic integration techniques and briefly examine some applications.
- https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_1_(Sklar)/05%3A_Integration/5.00%3A_Prelude_to_IntegrationIceboats are similar to sailboats, but they are fitted with runners, or “skates,” and are designed to run over the ice, rather than on water. Iceboats can move very quickly, and many ice boating enthu...Iceboats are similar to sailboats, but they are fitted with runners, or “skates,” and are designed to run over the ice, rather than on water. Iceboats can move very quickly, and many ice boating enthusiasts are drawn to the sport because of the speed. Iceboating is a popular winter sport in parts of the northern United States and Europe. (credit: modification of work by Carter Brown, Flickr) In this chapter, we first introduce the theory behind integration and use integrals to calculate areas.
- https://math.libretexts.org/Courses/Mission_College/MAT_3B_Calculus_II_(Kravets)/05%3A_Integration/5.00%3A_Prelude_to_IntegrationDetermining distance from velocity is just one of many applications of integration. In fact, integrals are used in a wide variety of mechanical and physical applications. In this chapter, we first int...Determining distance from velocity is just one of many applications of integration. In fact, integrals are used in a wide variety of mechanical and physical applications. In this chapter, we first introduce the theory behind integration and use integrals to calculate areas. From there, we develop the Fundamental Theorem of Calculus, which relates differentiation and integration. We then study some basic integration techniques and briefly examine some applications.
