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Math Help - Second Fundamental Theorem of Calculus!!

  1. #1
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    Second Fundamental Theorem of Calculus!!

    Find the derivative.


    i need help finding this, i dont know how to do it, thanks
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    Generally, you notice that the Derivative and the Integral are very closely related and you simply write down the answer.

    Think about (1+x)^{900}
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    Hello,

    Let F be an antiderivative of f.

    Then, \int_a^b f(t)dt=F(b)-F(a)

    According to it, what can you say ?
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    is up to his old tricks again! Jhevon's Avatar
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    In a nutshell. The second fundamental theorem of Calculus states:

    \frac d{dx} \int_c^x f(t)~dt = f(x)

    where c is a constant

    More generally (By the chain rule), \frac d{dx} \int_c^{g(x)}f(t)~dt = f(g(x)) \cdot g'(x)
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    Quote Originally Posted by Jhevon View Post
    In a nutshell. The second fundamental theorem of Calculus states:

    \frac d{dx} \int_c^x f(t)~dt = f(x)

    where c is a constant

    More generally (By the chain rule), \frac d{dx} \int_c^{g(x)}f(t)~dt = f(g(x)) \cdot g'(x)
    you're just gonna have to show me how to do it please, then i'll be able to understand better thanks
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mathlete View Post
    you're just gonna have to show me how to do it please, then i'll be able to understand better thanks
    you have the first case (c = 1), do you see that? your f(t) is (1 + t)^{900}, so your answer should be f(x). what would f(x) be?
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