(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the centroid of the region bounded by the curve x=5-y^{2}and x=0.

Answer is (2,0).

2. Relevant equations

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

3. 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!

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# Homework Help: Finding Centroid of Region

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