# Indefinite integral and average distance

#### -EquinoX-

1. The problem statement, all variables and given/known data

Find the average distance to the x-axis for points in the region bounded by the x-axis and the graph of y = x - x^2.

2. Relevant equations

3. The attempt at a solution

Can someone guide me how to solve this?

#### gabbagabbahey

Homework Helper
Gold Member
Pick any point in the region....what is the distance from that point to the x-axis?

If you had a finite number of points in the region, you would add up the distance from each point to the x-axis and divide by the number of points, correct?

Well, there are of course an infinite number of points in the region, so instead of adding, you integrate....

#### HallsofIvy

The "average value" of any function, f(x,y) on a region R is
$$\frac{\int_R f(x,y)dxdy}{area of R}$$

#### -EquinoX-

what is the area of R here? I already calculate the integral part

#### gabbagabbahey

Homework Helper
Gold Member
what is the area of R here? I already calculate the integral part
How do you usually calculate the area of a region?

#### Mark44

Mentor
How do you normally calculate the area of a region bounded by a curve and the x-axis? Have you made a sketch of the region?

#### -EquinoX-

yes I have made a sketch, it's an upside down parabola right? so I should do integration to find the area?

#### HallsofIvy

Yes, of course. You want
[tex]\frac{\int\int_R f(x,y)dydx}{\int\int_R dydx}[/itex]
where f(x,y) is the "distance to the x-axis".

#### -EquinoX-

okay got it. Thanks

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