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it is easy you can see any textbook........
Integration results in an equation which gives the area under the original equation between the bounds. Derivation results in an equation which gives the slope of the original line at any point.
See wikipedia article on polytropic processes.
The graph (on Cartesian coordinates) of a quadratic equation is a parabola.
in helmholtz vector equation why F=-∆ф+∆xA?