Fd the area bounded between the curves fx x2 - 4 and gx

Question

1. Find the area bounded between the curves f(x) = x² - 4, and g(x) = 4 - x².

2. Set up the integral to calculate the arc lenght of f(x) = Inx over the interval [1, 8].

Recall the Mean Value Theorem for Integrals (MVTi): If f is continuous on the interval [a, b], then there is at least one value of c in [a, b] such that

f(c) = {1/(b-a)} _a∫^b f(x) dx

3. Dose the MVTi apply to f(x) = 4 / x² on the interval [-4, -2]? If it applies, find the value(s) of guaranteed to exist by the theorem. If the MVTi does not apply, state why