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In this work on Riemann’s integral, we discuss the integral for real valued function defined and bounded on finite intervals and then also for unbounded functions in finite intervals. We also extended the notion of integrals in another dimension. The interval is replaced by a curve in two dimensional plane described by a vector valued function and the integrand is vector function defined and unbounded in this curve. The resulting integral is called the line integral or a contour integral and is denoted by or by some similar symbol where the dot purposely suggest an inner product of two vectors. The curve is called a path of integration.
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