Find the centroid of the region bounded by the curve x=5-y2 and x=0.
Answer is (2,0).
A = ∫[f(x)-g(x)]dx a->b
xbar = 1/A ∫ x[f(x)-g(x)]dx from a->b
ybar = 1/A ∫ 1/2[f(x)2-g(x)2]dx
The Attempt at a Solution
I know that the graph is a sideway parabola with vertex at (5,0) and bounded at x=0, this means that the graph is symmetrical above and below the x-axis so y value of centroid is 0.
For the x value of the centroid. I don't know if I should be integrating from 0->5? or integrating from the y intercepts -√5 -> √5.
In addition, I was always told it's the upper graph - lower graph. Because this is kind of a sideway graph, would I subtract parabola from line (5-y^2 - 0) or line from parabola (0-5-y^2)?
If anyone could help me understand setting the bounds, that would be great!