Integral Calculus

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Find the area lenght of the portion of the curve y=2x-x^2 with 0<=x<=2.

can you show me the solution and explain it deeper cause i don't know the concept.

thanks a lot.. :)

  • Integral Calculus -

    not sure what you mean by "area length"

    1. do you want the area of the parabola from x = 0 to x = 2, which is where the parabola cuts the x-axis?
    If so, then it would simply be
    Integral (2x - x^2)dx from 0 to 2
    = (x^2 - 1/3(x^3)│from 0 to 2
    = 4 - 8/3
    = 4/3

    2. Do you want the perimeter of that region?
    If so, then it would be the curved part of the parabola above the x-axis plus the straight line from 0 to 2

    find the arc length by following

    http://www.mathwords.com/a/arc_length_of_a_curve.htm

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