How boundary conditions help in finding integration constant

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Boundary conditions are essential for determining the value of the integration constant in indefinite integrals. By applying a known value of the integral at a specific point, such as I(a) at x=a, one can substitute this into the integral equation. This allows for the calculation of the constant C by rearranging the equation to isolate it. The process illustrates how boundary conditions provide necessary constraints that enable the solution of integration constants. Understanding this relationship is crucial for solving differential equations and applying mathematical models effectively.
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How to find value of integration constant?I know with the help of boundary conditions,but How boundary conditions help in finding integration constant?
 
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An integral ##I## without integration limits is an indefinite integral
$$
I(x) = \int f(x) dx = F(x) + C
$$
If you know at least one boundary condition, e.g. ##I(x)## at ##x=a##, you can plug in these values to get
$$
I(a) = F(a) + C
$$
which can be solved for C.
 
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