Confusion about the constant of integration and bounds

RandomMystery · Mar 26, 2011

When we integrate a derivative:

$gif.latex?\frac{dy}{dx}=&space;x^{5}+x^{4}+x^{3}.gif$

What are the bounds?

$gif.latex?\int_{?}^{?}dy=&space;\int_{?}^{?}x^{5}+x^{4}+x^{3}dx.gif$

Shouldn't we then have this if the bounds are x2 and x1:

$}{6}+\frac{x_{1}^{5}}{5}+\frac{x_{1}^{4}}{4}&space;\right&space;]&space;+&space;C.gif$

but instead we have this:

$f.latex?y=&space;\frac{x_{_{2}}^{6}}{6}+\frac{x_{2}^{5}}{5}+\frac{x_{2}^{4}}{4}+C.gif$

Samuelb88 · Mar 26, 2011

The constant of integration is a way of acknowledging that there are infinitely many solutions for every indefinite integral. When we integrate any function from [tex]x_1[/tex] to [tex]x_2[/tex] we are finding the area beneath the curve. Adding on a constant C would no longer give us the correct area beneath the curve, provided that C is not equal to zero.

Confusion about the constant of integration and bounds

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