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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