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Thread: integration help

  1. #1
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    integration help

    help pls

    a) if d^2y/d^2x = 6x+4 and dy/dx=8 and y=2 when x=1, find your site a function of x

    b) if f''(x)=x, f'(2)=1 and f (3)=0, find f (x)

    c) if f''(x) =-2x and the curve y=f (x) has a stationary point at (2,6), find the equation of this curve

    thank uu

  2. #2
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    Re: integration help

    Could you clarify the meaning of ‘the site of function of x’, for ‘a)’ ?

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    Re: integration help

    oh sorry - I meant "find y as a function of x"

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    Re: integration help

    For a)
    d^2y/d^2x = 6x+4
    dy/dx = 3x^2+4x+c1
    Since dy/dx=8 when x=1
    8 = 3(1)^2+4(1)+c1
    c1 = -5
    dy/dx = 3x^2+4x-5
    y = x^3+2x^2-5x+c2
    Since y=2 when x=1
    2 = (1)^3+2(1)^2-5(1)+c2
    c2 = 4
    Therefore y = x^3+2x^2-5x+4
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    Re: integration help

    For b)
    f''(x)=x
    f'(x)=x^2/2+c1
    Since f'(2)=1
    1=(2)^2/2+c1
    c1=-1
    f'(x)=x^2/2-1
    f(x)=x^3/6-x+c2
    Since f(3)=0
    0=(3)^3/6-(3)+c2
    c2=-3/2
    Therefore f(x)=x^3/6-x-3/2
    Last edited by darkk_blu; 5 Feb 2018 at 9:18 PM.
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    Re: integration help

    thank you for the help!! <3

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    Re: integration help

    Generally with these types of questions you should write out the primitive function including any unknown constants, then use the points that are given to you to figure out what the constants are.

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    Re: integration help

    Also "has a stationary point at (2,6)" implies that at x=2, y'=0 and at x=2, y=6

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