1. Find a function F(x, y) satisfying R= [0, 1] × [0, 4]. 8²F дхду - ¤ 6x²y and evaluate S S 6x²y dA for the rectangle
1. Find a function F(x, y) satisfying R= [0, 1] × [0, 4]. 8²F дхду - ¤ 6x²y and evaluate S S 6x²y dA for the rectangle
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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![1. Find a function F(x, y) satisfying
R= [0, 1] × [0, 4].
8² F
дхду
· 6x²y and evaluate S S 6x²y dA for the rectangle
2. Let f(x, y) = mxy², where m is a constant. Find a value of m such that S SR f (x, y) dA = 1,
where R = [0, 1] × [0, 2].
3. Compute the integral of f(x, y) = 1/lny over the domain D bounded by y = eº and
y = eva
4. Let f(y) be a function of y alone and set
G(t) = 66².
f(y) dy dx.
Use the Fundamental Theorem of Calculus to prove that G"(t) = f(t).
d
Hint: Let F(y) be a function such that
-F(y) = f(y); and evaluate the inner integral
dy
first.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F464fe16a-00d5-4182-8379-61bd4b8bbe02%2Fffa1d604-91d2-4ab0-8609-e051a4f936c3%2Fvh1zdp3_processed.png&w=3840&q=75)
Transcribed Image Text:1. Find a function F(x, y) satisfying
R= [0, 1] × [0, 4].
8² F
дхду
· 6x²y and evaluate S S 6x²y dA for the rectangle
2. Let f(x, y) = mxy², where m is a constant. Find a value of m such that S SR f (x, y) dA = 1,
where R = [0, 1] × [0, 2].
3. Compute the integral of f(x, y) = 1/lny over the domain D bounded by y = eº and
y = eva
4. Let f(y) be a function of y alone and set
G(t) = 66².
f(y) dy dx.
Use the Fundamental Theorem of Calculus to prove that G"(t) = f(t).
d
Hint: Let F(y) be a function such that
-F(y) = f(y); and evaluate the inner integral
dy
first.
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