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Internet Resources for the Calculus Student - Topics in Calculus


Definite  Indefinite  Antiderivatives F.T.C.
Techniques Numerical Improper Applications
Integration in ordinary language means putting things (or people) together, and it refers to the same sort of thing in mathematics as well.

The two most fundamental examples are the approximation of areas inside curved boundaries by sums of rectangles and triangles, and of the total distance covered in a trip by a sum of contributions from small time intervals on each of which the velocity is approximately constant.

Any quantity computed as a limit of such sums is called a Definite Integral.

The result of considering how such a quantity varies as we change one of the endpoints (eg to find the distance travelled up to time T for a moving object, or the 'area so far' under a function graph from a fixed left end starting point to a variable right end x) is called an Indefinite Integral.

And the connection between Indefinite Integrals and Antiderivatives is important enough to be known as the Fundamental Theorem of Calculus

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