It's a little hard to read this. Do you mean ? You can write this formula as follows: [tex]\int_0^4x(x^2-4)\,dx=32[/tex]. This is correct, but I don't see how it helps. The x-coordinate is .\int px(f1 - f2)dx

4,0\int x((x^2)-4)dx

and I got an answer of 32

It should be .then I did the M:

4,0\int ((x^2)-4)

and got an answer of 16/3

First, I calculated the areas under the parabola and found the area of the plate by subtracting those areas from 16. Second, the x-coordinate of the centroid is 0 because of the symmetry. (You can still calculate it using the general method, though.) Finally, the width of the plate at height y is , so the y-cooldinate of the centroid is . My answer is 12/5.