Integration can be used to calculate the area under a curve and the volume of solids of revolution.
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the example and solution of integral calculus
Just about all of calculus is based on differential and integral calculus, including Calculus 1! However, Calculus 1 is more likely to cover differential calculus, with integral calculus soon after. So there really isn't a right answer for this question.
Gottfried Leibniz is called the father of integral calculus.
Integral calculus was invented in the 17th century with the independent discovery of the fundamental theorem of calculus by Newton and Leibniz.
Its importance is tremendous - it has many different applications. Some of the applications include calculation of area, of volume, moment of inertia, of work, and many more.