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Math Help - integration problem

  1. #1
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    integration problem

    Given that \int_0^a(x-1)dx=\frac{1}{4}\int_0^a(x+2)dx,find the value of a.


    anyone help me please.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by mastermin346 View Post
    Given that \int_0^a(x-1)dx=\frac{1}{4}\int_0^a(x+2)dx,find the value of a.


    anyone help me please.
    Apply the Fundamental Theorem of Calculus to evaluate \int_0^ax-1\,dx and \tfrac{1}{4}\int_0^ax+2\,dx.

    At this point, \int_0^ax-1\,dx=\tfrac{1}{4}\int_0^a x+2\,dx will be an equation in terms of 'a'; at this point, you can solve for 'a'.

    Can you take it from here?
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  3. #3
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    Quote Originally Posted by Chris L T521 View Post
    Apply the Fundamental Theorem of Calculus to evaluate \int_0^ax-1\,dx and \tfrac{1}{4}\int_0^ax+2\,dx.

    At this point, \int_0^ax-1\,dx=\tfrac{1}{4}\int_0^a x+2\,dx will be an equation in terms of 'a'; at this point, you can solve for 'a'.

    Can you take it from here?
    hi,i have try many times,,but my answer not correct.
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  4. #4
    Newbie hungthinh92's Avatar
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    OK, just because you tried many times I will post the answer:
    \int_0^ax-1\,dx=\frac{1}{4}\int_0^ax+2\,dx
    \mid(x^2-x)\mid_0^a=\frac{1}{4}\mid(x^2+2x)\mid_0^a
    a^2-a=\frac{1}{4}(a^2+2a)
    After this, you should know how to solve by yourself.
    My answer will be: a=2 because a>0 \forall a\in R
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  5. #5
    Super Member General's Avatar
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    Quote Originally Posted by hungthinh92 View Post
    OK, just because you tried many times I will post the answer:
    \int_0^ax-1\,dx=\frac{1}{4}\int_0^ax+2\,dx
    \mid({\color{red} x^2}-x)\mid_0^a=\frac{1}{4}\mid({\color{red} x^2}+2x)\mid_0^a
    a^2-a=\frac{1}{4}(a^2+2a)
    After this, you should know how to solve by yourself.
    My answer will be: a=2 because a>0 \forall a\in R

    Its {\color{white}x}\frac{1}{2}x^2.
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  6. #6
    Newbie hungthinh92's Avatar
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    Its.
    I did a really big mistake... Now the answer will be:
    \frac{1}{2}a^2-a=\frac{1}{4}(\frac{a^2}{2}+2a)
    And then a = 4 instead of 2

    Thank General.
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