I have a question regarding the calculation of the area in part of a circle with a resource gradient.
I have some trouble with figuring out how to do this, and unfortunately couldn't find this on google or in other questions.
The problem is as follows: I want to calculate the amount of resources in part of a circle, see the picture below.
Calculating the area is easy, if I assume the distances are in meters, this is:
In this example:
However, I want to know the amount of resources (e.g. food or something like that) in this part of the circle. This is not constant, so it is not e.g. always 1 food item/m^2, in which case I could simply multiply the area by the resource density. Instead, it is a continuous gradient, from 0 food items/m^2 at the bottom to 1 food item/m^2 at the top.
To clarify: it is a continuous gradient, and therefore there can be 0 food items/m^2, 0.0001 food items/m^2, etc. The area is not divided into squares but continuous.
Of course, in this case, a much larger part of the circle has a low resource density, and only a small part has high resource density. If I could calculate the average, I would already be able to calculate the total amount of resources, but I cannot figure out how to do that.
Anyone who can help me with this? Would be much appreciated!