   # Applications of Integral Calculus

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Integral calculus is the study of mathematical integration dealing with integrals. These integrals, also known as area under the curve, are used to determine the following: areas, volumes, and lengths. There are a multitude of areas of real-world mathematics to which integral calculus is used. Integration is most often applied in physics, biology, and even chemistry. Integration is applied to physics in many situations. One important situation is finding the moment of inertia. The moment of inertia is the measure of the resistance of a rotating body to a change in motion. To find the moment of inertia, you find the area under, and also between the curve(s).
An application in which integration is key to reaching the target value is a PID Controller. The purpose of a PID Controller is to determine the error between what is measured and what is expected. The “I” or integration part of the controller is the collected past errors. The actual integral is the total of the instantaneous error over time. All parts of the error are included, meaning duration and amount.
Integral mathematics has much to do with the duration and amount of something. One major example is population analysis. Population analysis is a form of integral math that is applied for biology. The births in the present year rely on many things from previous years, most obviously the amount of births in the previous year. All things affect the population of the proceeding years. Since all variables intertwine with one another, they can be put into once common integral equation. Two major variables in the equation would be the rates of fertility and survivorship.
The average temperature for weather also uses integration. For example, the weatherman would note the average temperature for this time last year to show how much weather has fluctuated. How did he get an average temperature? He found it using integration. The weatherman would make a graph of the weather of math from this time last year,

Cited: www.intmath.com/applications_integration/6-moments-of-inertia.php en.wikipedia.org/wiki/PID_controller www.jstor.org/pss/1401794 www.jstor.org/pss/2235693 www.intmath.com/applications-integration/applications-integrals-intro.php biomaps.rutgers.edu/JCC_26_1752_2005.pdf people.hofstra.edu/Stefan_Waner/RealWorld/Calcsumm7.html

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