[Eclipse]

I can barely tell if this thread is genuine, but I'm looking for some core/mechanics help with something I can't find on the interwebs (Probably not looking hard enough not gonna lie.

So lets say I have a function that I can graph Euclid style. And I take the integral of the graph between the points a and b.

Is there a way such that I can find the X (call it m)coordinate where:

Spoiler:

https://latex.codecogs.com/gif.latex?%5C...f%28x%29dx

And the Y (call it n)coordinate where:

Spoiler:

https://latex.codecogs.com/gif.latex?%5C...%20%3D%20P
Where P is the definite integral of the graph under "y = n"
(I have no idea how to even express it)

Sorry, was away.

For your first question, assuming the area under the graph between x=b and x=m is equal to the area under the graph between x=m and x=a, and assuming you know the values of a and b, you could actually find the integral of y=f(x), and then substitute in the values and equate them.

i.e.
let g(x) be the function of the integral of f(x)
thus g(b) - g(m) = g(m) - g(a)

Then rearrange and solve for m. If you come out with a polynomial, you can find the discriminant and check if it's more than or equal to 0. If not, there's no point solving for m since there's no (real) solutions.

As for your second question, I actually don't know what you mean. Maybe clarify it a little?