Why do we have to add the +c when integrating a function
First of all it is important to know that differentiation is the opposite of integration. So if we integrate some function g(x) and get f(x), it means that when we differentiate f(x) we should get g(x). We demonstrate the importance of the +c with an example.Lets say we differentiate 3x. Our answer is 3If we differentiate 3x +3. Our answer is 3If we differentiate 3x +4. Our answer is 3So more generally, if we diferentaite 3x +c, where c is any constant, then we should get 3.Understanding that differentiation is the opposite of integration now shows that we must add the +c whenever we integrate a function. All the +c represents is that we don't know the constant that is at the end of the function.
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