Let I[0, 1], R+ = [0, ), 1 f(u, v) = 1+ uv g(x, y,t) =...
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Let I[0, 1], R+ = [0, ∞), 1 f(u, v) = 1+ u²v²¹ g(x, y,t) = f(x, t)f(y,t), (x, y, t) IX IX R₁ = 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 = [₂ (arctant) ² A =: (b) Using Tonelli's theorem on Ix I x R+ show that π 1 A - 1 = 7/7/₁₁ z 7 y drdy. 2 IxI x+y (c) Using Tonelli's theorem again show that A = ln 2. dt. Let I[0, 1], R+ = [0, ∞), 1 f(u, v) = 1+ u²v²¹ g(x, y,t) = f(x, t)f(y,t), (x, y, t) IX IX R₁ = 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 = [₂ (arctant) ² A =: (b) Using Tonelli's theorem on Ix I x R+ show that π 1 A - 1 = 7/7/₁₁ z 7 y drdy. 2 IxI x+y (c) Using Tonelli's theorem again show that A = ln 2. dt.
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Related Book For
Introduction to Real Analysis
ISBN: 978-0471433316
4th edition
Authors: Robert G. Bartle, Donald R. Sherbert
Posted Date:
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