   Practical use for Integrals and Infinate Series
  Hello everyone, I just finished a course on calc 2 (may have to retake it unfortunatly), but i was wondering what some common uses of integrals (anti derivates) and infinate series are.For example i know you can use integrals to find the volume and surface area of 3d objects.  Additionally it can be used to find the average value of things such as acceleration.What else are integrals useful and also infinate series? 
  They are used as a sumation over a continous function. Some uses in mechanics are finding centre's of mass, variable acceleration problems. Also it is used for probability density functions in stats.Also it is required to solve some differential equations which are common in many engineering tasks and also sciences.   [edited by - jamessharpe on August 1, 2003 2:22:50 PM];  Integrals and derivatives play heavily in physics based modeling. The theory of them was derived by Isaac Newton (and others) to explain the behaviour of the observed world (classical newtonian mechanics). Any 3D video game worth its salt nowadays has a decent physics engine and time-based movement. ;  Imagine having to do some physics problems without differentiation or integration. uhghh. ;  Solving a differential equation forward in time is essentially integration. Therefore the world of physics is full of integration.More "classical" integration can be seen in the field of computer graphics in the rendering equation, which is the key to all photorealistic images. It''s a hard recursive integral with both smooth parts and discontinuities. - Mikko Kauppila ;  An integral is an infinite serie, too.In physics, as other posters have pointed out, many, many problems are defined in terms of differential equations to solve. Another example is Newton''s heat diffusion law, which is proportional to the temperature difference between the object losing heat, and the environment (IIRC). You need integration to find the temperature of the object as a function of time.Cédric ;  yeah, another good one is:m*y'''' + c*y'' + k*y = forcing_functionwhich is a force balance of acceleration (y''''), damping (y''), and spring force (y) with an external force.  This describes how suspensions work, and is also applicable to circuits but i forget the analog (note the nerd-pun  since i''m in the mechanical side of engineering. ;quote:Original post by jermz  Isaac Newton (and others) Notably Leibniz, who is responsible for much of the notation we now use.  The extended S symol for integration for example.  Newtons developed the same methods at the same time, but crushed Keibniz as he had a more powerfull position ( namely president of the royal society ) at the time.