Explanation of Solution [² [²² The given integral is ydydx. Calculation: The given region is 0≤x≤2 and 0 ≤ y ≤x. Determine the value of r using the relation. x = rcos ( (1) Substitute 2 for x in Equation (1). 2 = r cos 0 r = 2 cos 8 r = 2 sec 0 Determine the value of using the relation. 0 = tan¹ (²) (2) Substitute 0 for x and 0 for y in Equation (2). 0 = tan-¹ () = tan-¹0 = 0 Substitute 2 for x and 2 for y in Equation (2). 0 = tan-¹ (²) = tan-¹1 = 4
Explanation of Solution [² [²² The given integral is ydydx. Calculation: The given region is 0≤x≤2 and 0 ≤ y ≤x. Determine the value of r using the relation. x = rcos ( (1) Substitute 2 for x in Equation (1). 2 = r cos 0 r = 2 cos 8 r = 2 sec 0 Determine the value of using the relation. 0 = tan¹ (²) (2) Substitute 0 for x and 0 for y in Equation (2). 0 = tan-¹ () = tan-¹0 = 0 Substitute 2 for x and 2 for y in Equation (2). 0 = tan-¹ (²) = tan-¹1 = 4
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
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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Transcribed Image Text:Explanation of Solution
[² [²²
The given integral is
ydydx.
Calculation:
The given region is 0≤x≤2 and 0 ≤ y ≤x.
Determine the value of r using the relation.
x = rcos (
(1)
Substitute 2 for x in Equation (1).
2 = r cos 0
r = 2
cos 8
r = 2 sec 0
Determine the value of using the relation.
0 = tan¹ (²) (2)
Substitute 0 for x and 0 for y in Equation (2).
0 = tan-¹ ()
= tan-¹0
= 0
Substitute 2 for x and 2 for y in Equation (2).
0 = tan-¹ (²)
= tan-¹1
= 4
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