The points where the 2 graphs intersect is where x = 0 and x = 2.
- 2 2
x = INT x dA / INT dA
0 0
INT dA = INT -x^2 + 4x + 3 - (x^2 + 3 ) dx = INT -2x^2 + 4x
= -2 x^3/3 + 2x^2
= 2.667 between 0 and 2
xdA = -2x^3 + 4x^2 INT xdA = -x^4/2 + 4x^3/3 = 2.667
centroid = 2.667 / 2.667 = 1 (x = 1)
The graphs of f and g intersect at x = 1, not x = -1.
g(x) is greater than f(x) for x < 1.
g(x) cannot be less than 1, as the graph flattens out at y = 1.
Based on the information given by the graph, the answer is "As the value of x increases, the value of g(x) will eventually exceed the value of f(x)".
I think it’s 36 square feet
Y = log3 27
27 = 3^x
3^3 = 27
so x = 3
