# Split the area

1. Apr 9, 2009

### epkid08

1. The problem statement, all variables and given/known data
Find the vertical line x = c such that it splits the area under curve f on the interval [a, b], into two equal parts.

2. Relevant equations

3. The attempt at a solution
I left the specifics out of the problem.

I see two ways to figure this out.

1. Find $$\frac{1}{2}\int^b_af dx$$ and set it equal to $$\int^c_a f dx$$ and solve for c.

2. Set $$\int^c_a f dx$$ equal to $$\int^b_c f dx$$ and solve for c.

Both ways seem like they should give the same answer, but unfortunately they don't. My question is which method is right and why?

2. Apr 9, 2009