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Math Help - integrals and constants

  1. #1
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    integrals and constants

    can someone explain why constants dont effect integrals? Isnt the integral of a constant the constant with an x after it ? : integral of 2 should be 2x, right? or wrong? why is this so?

    like the integral of 1/sqrt(2) * Dtheyta = 1/sqrt(2) * theyta (Dtheyta = derivitaive of theyta)
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  2. #2
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    Quote Originally Posted by frankinaround View Post
    can someone explain why constants dont effect integrals? Isnt the integral of a constant the constant with an x after it ? : integral of 2 should be 2x, right? or wrong? why is this so?

    like the integral of 1/sqrt(2) * Dtheyta = 1/sqrt(2) * theyta (Dtheyta = derivitaive of theyta)
    What do you mean by "constants don't effect integrals"? Unless you have some unusual meaning, they certainly do. If f(x)= g(x)+ C, then \int f(x)dx= \int g(x)+ Cx. That is, if f and g differ by the added constant, C, then their integrals differ by Cx.

    Perhaps you are mis-remembering that an added constant does not change the derivative. If f(x)= g(x)+ C, then \frac{df}{dx}= \frac{dg}{dx}.

    Or are you refering to the "constant of integration"? Because an added constant does not change the derivative, \int a d\theta= a\theta+ C where C can be any number because d(a\theta+ C)/d\theta= a for any C.
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