Finding the Vertical Line That Splits a Curve's Area in Two

[epkid08]

Homework Statement

Find the vertical line x = c such that it splits the area under curve f on the interval [a, b], into two equal parts.

Homework Equations

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?

 

[Billy Bob]

Both ways give same answer. Recheck your work.