posted by Akitsuke on .
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.. :)
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
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