independent variable

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Attention this is not a repeated talk, when one wants to  integrate f(x)=y it ends up with Y=F(x)+constant, we assume that the integration was could have been to carry out, if it is not we can say he or she is in trouble, and we call Y is the exact solution, it needs a boundary condition (Y,x) though to figure out the constant, you will find more in boundary condition types, x is an independent variable here and both y and Y are dependents, we are not finished yet, in case it was not could have been to carry out the required integration some go and imaging the interval of x and make an integration with two limits which is the fundamental, this is numerically with the computer sometime, everything is OK.