Let I[0, 1], R+ = [0, ), 1 f(u, v) = 1+ uv g(x, y,t) = f(x, t)f(y,t), (x, y, t) IX IX R = J. (a) Show that g is integrable on J (equipped with Lebesgue measure). Using Tonelli's theorem on R+ xIxI show that 2 1, gdtdxdy = [ (arctant) A =: (b) Using Tonelli's theorem on Ix I x R+ show that 1 A - 1 = 7/7/ z 7 y drdy. 2 IxI x+y (c) Using Tonelli's theorem again show that A = ln 2. dt.