Definite intergration area under curve bounded with line

  1. 1. The problem statement, all variables and given/known data

    A cruve has the equation [tex]y = x{3} - 8x^{2} + 20x [/tex]. The curve has stationary points A and B. There is a line through B parallel to y axis and meets the x axis at the point N. The region R is bounded by the curve , the x-axis and the line from A to N. Find the exact area under the curve

    2. Relevant equations

    3. The attempt at a solution

    Well I found the x co-ords of A and B, which is [tex]\frac{10}{3}[/tex] or 2. I intergrated the curve and got

    [tex]\frac{4x^{3}}{4} - \frac{8x^{3}}{3}+10x^{2}[/tex]

    no +C as we'll be having limits i presume

    But i dont know how to get the area of region R... as there is a stupid line in the way!!!

    Can somebody show/help me to do it.

    Thanks :)
  2. jcsd
  3. Hey

    My first advice is to a picture of your problem. After that you notice that the exercise is to calculate the integral from x=A to x=B of f, i.e. integration of a polynomial. I expect you know how to do that.
  4. i can intergrate a polynominal easily and in the question paper there is a picture of the question. But because of this AN line, it's thrown me. How would you go about doing it.

  5. tiny-tim

    tiny-tim 26,016
    Science Advisor
    Homework Helper

    Hi thomas! :smile:

    If I've understood the question right, all you have to do is add a triangle (whose area is obvious), and you get the standard integral. :smile:
  6. ahhh i see cheerz :)
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