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Math Help - Integrals

  1. #1
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    Integrals

    Whats the difference between dt and dx?

    F(X) = e^x + ∫ sin t dt

    F(X) = e^x + ∫ sin t dx

    Then calculate F`(π)

    ∫ is 1 and x.

    Somebody who can explain this kind of integrals shortly? why dt and not dx?
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  2. #2
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    Re: Integrals

    t is just a dummy variable.

    Fundamental theorem of calculus ...

    \frac{d}{dx} \left[\int_a^x f(t) \, dt \right] = f(x)
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  3. #3
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    Re: Integrals

    ok, so if i understand you correct

    ∫ sin t dt <=> ∫ sin x dx

    its just an other way to whrite it?
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  4. #4
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    Re: Integrals

    Quote Originally Posted by ronaldopeter View Post
    Whats the difference between dt and dx?

    F(X) = e^x + ∫ sin t dt

    F(X) = e^x + ∫ sin t dx

    Then calculate F`(π)

    ∫ is 1 and x.

    Somebody who can explain this kind of integrals shortly? why dt and not dx?
    were these meant to be different functions, F(x) ?
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