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Does an integral find the net of infinitesimal or does it only add its magnitude. For example in case of vectors, in a case the sin component of gravitational field was getting cancelled but when I integrated the sin component of a body of mass dm in a continuous body the answer came non zero. Also as an integral is just a summation, I think it just adds the magnitude. Am I correct?

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  • $\begingroup$ Typically an integral is visualized as summing the area underneath a curve by adding up infinitesimally narrow strips $\displaystyle \int f(x)dx \approx \sum f(x) \Delta x$. Line integrals find the length of curved lines by adding infinitesimally small straight line segments. Area or length is an interpretation of the physical problem the math is abstract. Sometimes real world models help other times they don't. $\endgroup$
    – user186104
    Jun 29, 2020 at 6:43

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