Please do both of the following. i. Suppose f and g are integrable functions on a rectangle R C R^n, and 9 < f. Prove that ∫R gdV < ∫R fdV.
ii. Suppose Ώ is a region, and f is continuous on Ώ. Let M = sup(ſ) and m = inf(f), where these are taken over all inputs in Ώ. Prove that m. vol(Ώ) < ∫ Ώ fdV < M . vol(Ώ).