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Math Help - Integration help

  1. #1
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    Integration help

    suppose , find f'(Pi^(1/3))

    Im not sure weather i integrate or diffrenciate.
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by geurrp the yard View Post
    suppose , find f'(Pi^(1/3))

    Im not sure weather i integrate or diffrenciate.
    This is an application of the chain rule. Say that F(y)=\int\sin(5y)\,dy. Thus, we are given that f(t)=F(-t^3)-F(3).

    Now take the derivative. (Remember, F(3) is a constant, so its derivative is 0.)

    f'(t)=\underbrace{F'(-t^3)=\sin(5\cdot-t^3)\cdot\frac{d}{dt}[-t^3]}_{chain~rule}=\sin(-5t^3)\cdot-3t^2=\boxed{3t^2\sin(5t^3)}

    (Recall that sine is an odd function so \sin(-5t^3)=-\sin(5t^3).)
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  3. #3
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    Hi, Why dont you integrate that sin5y function?
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  4. #4
    Super Member redsoxfan325's Avatar
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    You could if you wanted to, but it would be unnecessary work as you would be differentiating again immediately. Also, don't forget to plug \sqrt[3]{\pi} into the boxed equation.
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  5. #5
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    Im just a little confused, when I see a integral sign, I automaticaaly assume to integrate. Also why did you not find the derviative of sin?
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  6. #6
    Super Member redsoxfan325's Avatar
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    \frac{d}{dx}\left[\int f(x)\,dx\right]=f(x)

    You don't need to integrate and differentiate to know that's true.
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  7. #7
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    Hi when i sub in cube root of Pi into the equation I get zero. Because sin5(pi)Is that correct?
    Last edited by geurrp the yard; October 13th 2009 at 02:31 PM.
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  8. #8
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    Yes I agree
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