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Math Help - Having trouble simplifying this integral

  1. #1
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    Having trouble simplifying this integral

    So I have to evluate the integral and simplify it. I'm stuck near the end after applying F(b) - F(a) and can't simplify it further.
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  2. #2
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    \displaystyle \int (y^2-\sin y)~dy =\frac{y^3}{3}+\cos y \neq \frac{y^3}{3}-\cos y
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  3. #3
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    Wait so it's + cos y and not - cos y? But to get -sin y it has to be -cos y.
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  4. #4
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    Quote Originally Posted by solidstatemath View Post
    Wait so it's + cos y and not - cos y? But to get -sin y it has to be -cos y.
    I understand it as

    \displaystyle \frac{d}{dy}\sin y =\cos y

    and

    \displaystyle \frac{d}{dy}\cos y =-\sin y

    therefore

    \displaystyle \int-\sin y ~dy = \cos y +C
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  5. #5
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    I'm having trouble simplifying this.

    I got:

    [(4pi/5)^3 / 3] - [COSpi4/5] - [(-4pi/5)^3 / 3] - [-COS(-4pi/5)]

    I think the COS term will cancel out and then we get 2[(4pi/5)^3 / 3] as the answer.

    Things I am not sure about: the signs. I'm not sure about:

    - [-COS(-4pi/5)] *** does this become positive? What about the -4pi/5?
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  6. #6
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    Okay I think I got it, the COS part cancel out leaving just the 4pi/5 parts.

    My end result is then:

    [(4pi/5)^3 / 3] + [(4pi/5)^3 / 3]

    I am trying to simplify this and have some trouble. I turned it into:

    2 * [(4pi/5^3) * 3]

    Can it be simplified further?
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  7. #7
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    Quote Originally Posted by solidstatemath View Post
    I'm having trouble simplifying this.

    I got:

    [(4pi/5)^3 / 3] - [COSpi4/5] - [(-4pi/5)^3 / 3] - [-COS(-4pi/5)]

    I think the COS term will cancel out and then we get 2[(4pi/5)^3 / 3] as the answer.

    Things I am not sure about: the signs. I'm not sure about:

    - [-COS(-4pi/5)] *** does this become positive? What about the -4pi/5?
    cosine is an even function ... \cos(-x) = \cos(x)
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  8. #8
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    Skipping the details here, the format above would then be the first term with pi - cosine term + second pi term + second cosine term.

    The is the most I can simplify it: 2 * [(4pi/5^3) * 3]

    How does this look? Basically the cosine terms cancel out and leaves just 2 times the pi terms.
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