2. Let E be a Jordan region in Rn and

f, 9 be integrable on E with Lf(X)dx= 5 and L9(X)dx= 2.

(a) Find Lo (2f(x) - 3g(x)) dx, L (2f(x) - 3g(x)) dx, and h(2f (X) - 3g(x)) dx.

(b) If h is integrable on E and g(x) ::; h(x) ::; f(x), prove that JE h(x) dx =1= 7f /2.

(c) Suppose that n = 2 and E <;;;; [0,1] x [0,1]. If g(x, y) ::; f(x, y) for all

(x, y) E E, prove that there is a a ::; to ::; 1 such that L x2(f(x, y) - g(x, y)) dA = 3to·