Problem: Define the rectangles

$\displaystyle R_n = [0, (n-1)/n]$ X $\displaystyle [0, (n-1)/n] = \{(x,y): 0 \leq x \leq (n-1)/n$ and $\displaystyle 0 \leq y \leq (n-1)/n \}$

Also define R = [0,1] X [0,1]. Suppose f is a bounded function on R and that f is integrable over each $\displaystyle R_n$.

(a) Prove that f is integrable over R.

(b) Define the integrals

$\displaystyle I_n = \int\int _R_n f dA$ and $\displaystyle I = \int\int _R f dA $

Prove that $\displaystyle \lim n \rightarrow \infty I_n = I$

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Can I get a hint on how to start (b)?