Definition of setting the integration constant equal to zero.In Calculus books, we often hear of setting the integration constant equal to zero. But what does that actually mean? For example, the set of antiderivatives of 2x is x 2 + C. If we set the constant equal to zero, we get simply x 2 . However, I can also write the set of antiderivatives as x 2 + π + C. In that case, setting the constant equal to zero would give us x 2 + π. So, my question is, what does setting the constant equal to zero in an antiderivative actually mean?

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Definition of setting the integration constant equal to zero.In Calculus books, we often hear of setting the integration constant equal to zero. But what does that actually mean? For example, the set of antiderivatives of 2x is       x    2    +  C. If we set the constant equal to zero, we get simply       x    2  . However, I can also write the set of antiderivatives as       x    2    +  π  +  C. In that case, setting the constant equal to zero would give us       x    2    +  π. So, my question is, what does setting the constant equal to zero in an antiderivative actually mean?

gozaderaradiox5 · Accepted Answer

Explanation:Only when it is clear which copy of C is intended—i.e., only in a situation where a specific antiderivative has been specified and we want to agree not to add an additive constant to it—does &quot;setting the integration constant to zero&quot; make sense.Another example to supplement yours:  −  arccos  ⁡  x  +      C    1    =  ∫                    d            x              1      −              x        2              =  arcsin  ⁡  x  +      C    2    ,    −  arccos  ⁡  x  ≠  arcsin  ⁡  x  .

Definition of setting the integration constant equal to zero. In Calculus books, we often hear of s

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