Let F(x, y) = x1exy. Show that 2 F/x y = yexy and use the result

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Let F(x, y) = x−1exy. Show that ∂²F/∂x ∂y = yexy and use the result of Exercise 52 to evaluate SSR" yexy da for R = [1, 3] × [0, 1].

Data From Exercise 52

Prove the following extension of the Fundamental Theorem of Calculus to two variables: If ∂²F/∂x ∂y = ƒ(x, y), then

f R f(x,y) dA= F(b,d) - F(a,d) - F(b,c) + F(a, c)

where R = [a, b] × [c, d].

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Let F(x, y) = x1exy. Show that 2 F/x y = yexy and use the result

Question:

SSR" yexy da

Step by Step Answer:

Differentiating Fx y xey with respect to y gives F xlery dy y We no...View the full answer

Calculus

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