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Why does an answer to an integration problem involve a Constant of Integration?
Wiki User
∙ 8y ago
The indefinite integral is the anti-derivative - so the question is, "What function has this given function as a derivative". And if you add a constant to a function, the derivative of the function doesn't change. Thus, for example, if the derivative is y' = 2x, the original function might be y = x squared. However, any function of the form y = x squared + c (for any constant c) also has the SAME derivative (2x in this case). Therefore, to completely specify all possible solutions, this constant should be added.
Wiki User
∙ 8y ago
Wiki User
∙ 8y agoSince the derivative of a constant is zero, the integration involves a constant
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I'm assuming you are asking why you cannot work through your simplification and only put a constant on the last line. The simplest answer is that mathematicians are picky people, and when working through a problem EVERY line must make absolute mathematical sense. Leaving the constant off until the last line makes every line between the point where the integration occurs and the last line false. (Unless you are lucky and the constant of integration is 0, however this still needs to be proven)
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