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One of the major applications of indefinite integrals is to calculate definite integrals. If you can't find the indefinite integral (or "antiderivative") of a function, some sort of numerical method has to be used to calculate the definite integral. This might be seen as clumsy and inelegant, but it is often the only way to solve such a problem.

Definite integrals, in turn, are used to calculate areas, volumes, work, and many other physical quantities that can be expressed as the area under a curve.

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Q: What are some real life applications of indefinite integrals?
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