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Math Help - Anti-differentiation

  1. #1
    Member Awsom Guy's Avatar
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    Anti-differentiation

    I can't do this questio although my teacher helped me I still can't do it, please check.

    y''= x+2 and if x=3, y'=7 and y=12.
    (hint: evaluate constants as they are created)

    My failed attempt:

    y'=(x^2)/(2) + 2x + C = 7 when x=3.
    9/2 + 6 + C=7
    C=-3.5

    And I also know that (x^3)/(6) +x^2 +7 = 12
    That is the second derivative.
    I hope what I have written makes sense.
    Thanks
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  2. #2
    Senior Member
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    Quote Originally Posted by Awsom Guy View Post
    I can't do this questio although my teacher helped me I still can't do it, please check.

    y''= x+2 and if x=3, y'=7 and y=12.
    (hint: evaluate constants as they are created)

    My failed attempt:

    y'=(x^2)/(2) + 2x + C = 7 when x=3.
    9/2 + 6 + C=7
    C=-3.5

    And I also know that (x^3)/(6) +x^2 +7 = 12
    That is the second derivative.
    I hope what I have written makes sense.
    Thanks
    we have y' = (x^2)/(2) + 2x - 3.5

    then

    y = (x^3)/(6) +x^2 - 3.5x + K

    when x = 3

    12 = (3^3)/(6) +3^2 - 3.5(3) + K
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  3. #3
    Member Awsom Guy's Avatar
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    Quote Originally Posted by dedust View Post
    we have y' = (x^2)/(2) + 2x - 3.5

    then

    y = (x^3)/(6) +x^2 - 3.5x + K

    when x = 3

    12 = (3^3)/(6) +3^2 - 3.5(3) + K
    Wait where did the K come from, sorry I dont follow.
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  4. #4
    Member Awsom Guy's Avatar
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    I am soooo sorry for being dumb...de dust has given me what I have to do thanks.
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  5. #5
    Senior Member
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    Quote Originally Posted by Awsom Guy View Post
    Wait where did the K come from, sorry I dont follow.
    another constant from the indefinite integral.
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