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21. Suppose that f(x, y) can be written as a product f(x, y) = F(x)G(y) of a function of x and a function of y. Then the integral of f over the rectangle R: a < x < b, c < y< d can be evaluated as a product as well, by the formula f(x, y) dA F(x) dx G(y) dy ). (1) The argument is that || f(x, y) dA = F(x)G(y) dx ) dy (i) F(x) dx ) dy (ii) F(x) dx ) G(y) dy (iii) x)/ Gợ) dy. F(x) dx (iv) a. Give reasons for steps (i) through (iv). When it applies, Equation (1) can be a time-saver. Use it to evaluate the following integrals. cIn2 /2 b. ГГ e cos y dy dx c. dx dy

21. Suppose that f(x, y) can be written as a product f(x, y) = F(x)G(y) of a function of x and a function of y. Then the integral of f over the rectangle R: a < x < b, c < y< d can be evaluated as a product as well, by the formula f(x, y) dA F(x) dx G(y) dy ). (1) The argument is that || f(x, y) dA = F(x)G(y) dx ) dy (i) F(x) dx ) dy (ii) F(x) dx ) G(y) dy (iii) x)/ Gợ) dy. F(x) dx (iv) a. Give reasons for steps (i) through (iv). When it applies, Equation (1) can be a time-saver. Use it to evaluate the following integrals. cIn2 /2 b. ГГ e cos y dy dx c. dx dy

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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21. Suppose that f(x, y) can be written as a product f(x, y) = F(x)G(y) of a function of x and a function of y. Then the integral of f over the rectangle R: a < x < b, c < y< d can be evaluated as a product as well, by the formula f(x, y) dA F(x) dx G(y) dy ). (1) The argument is that || f(x, y) dA = F(x)G(y) dx ) dy (i) F(x) dx ) dy (ii) F(x) dx ) G(y) dy (iii) x)/ Gợ) dy. F(x) dx (iv) a. Give reasons for steps (i) through (iv). When it applies, Equation (1) can be a time-saver. Use it to evaluate the following integrals. cIn2 /2 b. ГГ e cos y dy dx c. dx dy
Transcribed Image Text:21. Suppose that f(x, y) can be written as a product f(x, y) = F(x)G(y) of a function of x and a function of y. Then the integral of f over the rectangle R: a < x < b, c < y< d can be evaluated as a product as well, by the formula f(x, y) dA F(x) dx G(y) dy ). (1) The argument is that || f(x, y) dA = F(x)G(y) dx ) dy (i) F(x) dx ) dy (ii) F(x) dx ) G(y) dy (iii) x)/ Gợ) dy. F(x) dx (iv) a. Give reasons for steps (i) through (iv). When it applies, Equation (1) can be a time-saver. Use it to evaluate the following integrals. cIn2 /2 b. ГГ e cos y dy dx c. dx dy
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