Hey! First of all, thank you for those who have set up this forum, I'm really happy that helpful online communities like this exist. 
I hope I can be of help too in the future, but now I'm here with a bit of a problem!
We are currently dealing with applications of integration in our calculus course, and one of our homework problems is giving me a bit of a headache.
You are given two functions: f(x) = 2x*sqrt(x) and g(x) = -2x + 24 that intersect at points (4, 16).
One of the questions goes as follows: Find the center of gravity of the area bounded by the two axes and the graph of g(x).
I am not sure how to find the initial area.
I found that when an area is bounded by an axis and a function, then the axis sets the lower boundary as 0. But indeed, that isn't the case here. The solution to the homework is given that the A = 1/2 * 12 * 24 = 144, and the integral boundaries are 0 to 12, but I'm honestly not sure where this solution comes from.
I'm pretty sure that the solution is D'Oh simple, but my brain just isn't picking up the pieces now. :roll: If you could give me a bit of a kick in the right direction so that I can figure out why is how and what, I would appreciate it so much!
Thank you!
I hope I can be of help too in the future, but now I'm here with a bit of a problem!We are currently dealing with applications of integration in our calculus course, and one of our homework problems is giving me a bit of a headache.
You are given two functions: f(x) = 2x*sqrt(x) and g(x) = -2x + 24 that intersect at points (4, 16).
One of the questions goes as follows: Find the center of gravity of the area bounded by the two axes and the graph of g(x).
I am not sure how to find the initial area.
I found that when an area is bounded by an axis and a function, then the axis sets the lower boundary as 0. But indeed, that isn't the case here. The solution to the homework is given that the A = 1/2 * 12 * 24 = 144, and the integral boundaries are 0 to 12, but I'm honestly not sure where this solution comes from.
I'm pretty sure that the solution is D'Oh simple, but my brain just isn't picking up the pieces now. :roll: If you could give me a bit of a kick in the right direction so that I can figure out why is how and what, I would appreciate it so much!
Thank you!