### Activity Definite Integrals

Check us out at http://www.tutorvista.com//videos A definite integral is an integral with upper and lower limits. If is restricted to lie on the real line, the definite integral is known as a Riemann integral (which is the usual definition encountered in elementary textbooks). However, a general definite integral is taken in the complex plane, resulting in the contour integral with , , and in general being complex numbers and the path of integration from to known as a contour. The first fundamental theorem of calculus allows definite integrals to be computed in terms of indefinite integrals, since if is the indefinite integral for a continuous function , then This result, while taught early in elementary calculus courses, is actually a very deep result connecting the purely algebraic indefinite integral and the purely analytic (or geometric) definite integral. Definite integrals may be evaluated in Mathematica using Integrate[f, x, a, b ]

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