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The Difference Between Two Indefinite Integrals

  1. Dec 30, 2014 #1
    I actually came across this question on social media. What is:

    $$\int sin (x) \, dx - \int sin (x) \, dx$$

    And I think the answer depends on how we interpret:

    $$\int sin (x) \, dx$$

    If we think of it as a single antiderivative, the answer would be zero. If we think of it as being representative of several antiderivatives of ##sin (x)##, the answer would be some arbitrary constant.

    What do you think?
    Last edited: Dec 30, 2014
  2. jcsd
  3. Dec 30, 2014 #2


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    I think "define non-standard or unclear notation if you use it".
  4. Dec 30, 2014 #3
    It's standard to evaluate indefinite integrals as the anti derivative of the function plus a constant of integration.

    So I think ∫sin(x) dx-∫sinx(x) dx would just be equal to an arbitrary constant (as you said).
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