Posted by **Akitsuke** on Monday, September 15, 2008 at 10:45am.

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 -
**Reiny**, Monday, September 15, 2008 at 11:00am
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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