(a) Evaluate the double integral Je emax{z²,y²} where R = {(x, y) |0 ≤ x ≤ 1,0 ≤ y ≤ 1} is the unit square and max{x², y²}: dA, r², if x² ≥ y², y², if y² ≥ x². = - (Hint: Split R into two appropriate pieces.)

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(a) Evaluate the double integral
Je emax{z²,y²}
where R = {(x, y) |0 ≤ x ≤ 1,0 ≤ y ≤ 1} is the unit square and
max{x², y²}:
=
dA,
[x², if x² ≥ y²,
>
y², if y² > x².
(Hint: Split R into two appropriate pieces.)
(b) Evaluate the improper iterated integral
1
[ S (x² + y²) arctan(y/2)² +1′
dy dx.
Transcribed Image Text:(a) Evaluate the double integral Je emax{z²,y²} where R = {(x, y) |0 ≤ x ≤ 1,0 ≤ y ≤ 1} is the unit square and max{x², y²}: = dA, [x², if x² ≥ y², > y², if y² > x². (Hint: Split R into two appropriate pieces.) (b) Evaluate the improper iterated integral 1 [ S (x² + y²) arctan(y/2)² +1′ dy dx.
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