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Math Help - Definite integral problem

  1. #1
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    Definite integral problem

    The diagram above shows the curve y=2x^2-5x+5 and straight line y=5-x.Find

    (a)the points if intersection of the two graphs

    i get the answer (0,5)(2,3)

    (b)The area of the shaded region.
    Attached Thumbnails Attached Thumbnails Definite integral problem-definite-integral.png  
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  2. #2
    Senior Member Stroodle's Avatar
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    I've never really solved a problem like this before (or any integration problem actually) but would this work:

    \int_{0}^{3} 5-x\ dx-\left(\int_{0}^{3}5-x\ dx\ -\ \int_{0}^{3}2x^2-5x+5\ dx \right )

    Then do a similar thing for x\in \left [ 3,5\right ] and add the results together.
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  3. #3
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    this is my step to get the answer but the answer provided not same with my answer

    \frac{1}{2}(5)(5) - \left(\int_{0}^{5}(2x^2-5x=5) dx
    =\frac{25}{2}-(\frac 2{x^3}{3}-\frac{5x^2}{2})_0^5
    =\frac{25}{2}-({2(5)^3}{3}-\frac{5(2)^2}{2}=5(5))-0
    =\frac{25}{2}-(\frac{275}{6}
    =\frac{-33}{1}{3}

    is that correct??lol,my latex is wrong
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  4. #4
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    You can do this way.
    [Intg(5 - x)*dx between 0 to 5 -[ Inte(2x^2 -5x + 5)*dx] between 0 to 3.
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