The discussion revolves around calculating the average height above the x-axis for points within a specified region defined by the inequalities 0 <= x <= 1 and 0 <= y <= x^2, within the context of multivariable calculus.
There is an ongoing exploration of the definition of height in this context, with some participants offering guidance on setting up the integral while others seek clarification on the reasoning behind using the y-coordinate as height.
Participants are navigating the definitions and assumptions related to the average height and the integration process, with some uncertainty about the terminology used in the problem statement.
mahrap said: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 said: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 said:Why would the height be y though? That's what i don't understand