# Polynomial integral

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

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#### Anton

Created: 2021-09-02 08:25:37, Last updated: 2021-09-02 08:25:37

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.

#### 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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