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Polynomial integral

The calculator integrates a univariate polynomial and calculates an integration constant by a point.

This calculator integrates a polynomial function. In addition, it calculates the integration constant if you provide a point lying on the graph of the result function.

PLANETCALC, Polynomial integral

Polynomial integral

The polynomial coefficients, space separated, in order from higher term degree to lower
Calculate the integration constant by the point
Input polynomial
 
Result
 



An indefinite integral of a polynomial function defined by the coefficients a0 .. an, can be calculated by the formula below:
I(x) = \int{\sum_{i=0}^n{a_i x^i}}=\sum_{k=1}^{n+1}{\frac{a_{k-1} x^k}{k}}+C
If you know point coordinates (x0,y0) , belonging to the result function graph, you can calculate the integration constant С in the following way:
C = y_0-\left(\sum_{k=1}^{n+1}{\frac{a_{k-1} x_0^k}{k}}\right)

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