Average value of x-coord and y-coord in a semicircle. multivariable calculus.

[mahrap]

Calculate the average height above the x-axis of a point in the region 0 <= x <= 1 , 0 <= y <= x^2. I don't know what function to use to find the average height.

 

[Dick]

Calculate the average height above the x-axis of a point in the region 0 <= x <= 1 , 0 <= y <= x^2. I don't know what function to use to find the average height.

I expect height means y. So you want to integrate y over the region then divide by the area of the region. Set it up as a double integral of y.

 

[mahrap]

I expect height means y. So you want to integrate y over the region then divide by the area of the region. Set it up as a double integral of y.

Why would the height be y though? That's what i don't understand

 

[Dick]

Why would the height be y though? That's what i don't understand

y is the distance of a point (x,y) to the x-axis. They are just calling that 'height'.