Thread: limits of double integration

1. limits of double integration

the question is:

Find the average distance to the x-axis for points in the region bounded by the x-axis and the graph of y = x - x2.

i know that it has a shape kind of like a circle and x goes from 0 to 1 and y has to go from 0 but i dont understand how to get the upper limit and the area (R).

2. Originally Posted by acosta0809
the question is:

Find the average distance to the x-axis for points in the region bounded by the x-axis and the graph of y = x - x2.

i know that it has a shape kind of like a circle and x goes from 0 to 1 and y has to go from 0 but i dont understand how to get the upper limit and the area (R).

the curve is parabolic.

$x - x^2 = 0$

$x(1 - x) = 0$

lower limit, $x = 0$

upper limit, $x = 1$

$R = \int_0^1 x - x^2 \, dx$