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Math Help - antiderivative question - help

  1. #1
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    antiderivative question - help



    for
    a. i get:
    local max: 2.5*pi
    local min: 1.5*pi

    b. global max: 3.5pi
    global min: 2pi/3

    are a and b right?

    c. how to do this?

    d. by the fundamental theorem of calculas (for this question) g'(x)=f(x) so i will have to find the antiderivative of g'(x).. but whats the antiderivative of xsinx? i dont know how to get it..
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  2. #2
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    Quote Originally Posted by Baatata View Post
    but whats the antiderivative of xsinx? i dont know how to get it..
    you need to employ integration by parts which says

    \int uv' = uv - \int vu'

    in your case make u = x and v' = \sin(x)
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  3. #3
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    Quote Originally Posted by Baatata View Post


    for
    a. i get:
    local max: 2.5*pi
    local min: 1.5*pi

    b. global max: 3.5pi
    global min: 2pi/3

    are a and b right?

    c. how to do this?

    d. by the fundamental theorem of calculas (for this question) g'(x)=f(x) so i will have to find the antiderivative of g'(x).. but whats the antiderivative of xsinx? i dont know how to get it..
    It seems to me that \int_0^xf(t)dt=\int_0^xt\sin{t}dt and by parts we have

    g(x)=\int_0^xt\sin{t}dt=-t\cos{t}\Big|_0^x+\int_0^x\cos{t}dt. So, now employ the FTC.
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  4. #4
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    could you guys break it down for me? i have no idea what you did there..
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  5. #5
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    \int uv' = uv - \int vu'

    in your case make u = x and v' = \sin(x)

    Go and find

    v = \int \sin(x) and u' = \frac{d}{dx}~x

    Sub these into

    \int uv' = uv - \int vu'

    ....

    Vonnemo has given you the answer to this in his response.
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  6. #6
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    i kinda get it even though i cant figure out how u came up with this forumla

    but anyways.. back to the original question, once i found the antiderivative, what do i have to do next?
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  7. #7
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    Quote Originally Posted by Baatata View Post
    i kinda get it even though i cant figure out how u came up with this forumla
    This formula comes from the product rule of differentiation.

    Recall

    (uv)' = uv'+vu'

    If you integrate both sides of this equation you get the formula I gave you.


    Quote Originally Posted by Baatata View Post

    but anyways.. back to the original question, once i found the antiderivative, what do i have to do next?
    You sub in the terminals
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  8. #8
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    well i just had some help from my friend and he said that i dont even need g(x).

    so g'(x) = xsinx.
    g'(x) = 0 when x=0,pi, 2pi, 3pi, 4pi
    how do i figure out which on is local min/max and global min/max?
    i know that when it changes from + to - its local max but what about global max? when would that be?
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