What is the meaning of integral geometric interpretation


What is the meaning of integral (geometric interpretation, etc.) and how is it different from derivative? What are some applications of integrals? Pick one of options below to answer.You can use S to stand for integral.

1) Provide an example of U-substitution or a shortcut to compute an integral

2) Provide an example of an application of integral (business, economics, social sciences, etc.) and show how to work it out.

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Mathematics: What is the meaning of integral geometric interpretation
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