I have a set of discrete (x,y) points and need to find the area between the curve and the y-axis. However, the curve seems to be a multi-valued function (multiple x for the same y). Is such an operation valid, and if so, how?
edit: The image of the curve is in the link above. Kindly take a look.
I tried to do trapezoidal integration for this in MATLAB and got a negative answer. What is the interpretation of this negative area (even when all data are positive)? To check if area becoming negative was wrong, it tried doing the integration as ($xy - \int ydx$). I got the same answer in both cases.
This shows the area that I need when multiple x occurs for a single y. Area for all x is required.