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

Question

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

thanks a lot.. :)

Answer 1

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