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If definite integration of a plane curve y=f(x) from a to b gives the area bounded by the curve, the x axis and the lines x=a and x=b then what does indefinite integral of f(x) represents. I know that it represents a family of curves but i couldnt graphically build up a connection between these two. Doesn't it represent some sort of area function just like definite integral. What exactly is the basic difference between these two. Plz explain elborately

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  • $\begingroup$ Maybe you are confused because they both use the integral sign $\int $. The connection between the two should become apparent once you know the Fundamental Theorem of Calculus. and btw, the definite integral gives the ``net'' area, not just area. $\endgroup$ – Isko10986 Nov 20 '16 at 5:35
  • $\begingroup$ The indefinite integral gives a family of functions whose derivative is the integrand. The concepts of indefinite and definite integration are closely linked by the fundamental theorem of calculus. $\endgroup$ – Kaj Hansen Nov 20 '16 at 5:36
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An indefinite integral is an integral without upper and lower limits, and it yields the general set of functions known as antiderivatives of the integrand. The first fundamental theorem of calculus gives the connection between indefinite and definite integrals; I believe reading into the theorem will answer your questions

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