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Evaluate the following integral, where R is bounded by x = 1, y = 2x + 4, and y=-x-2. SS₂² dA R

Evaluate the following integral, where R is bounded by x = 1, y = 2x + 4, and y=-x-2. SS₂² dA R

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.2: Substitution
Problem 8E: Use substitution to find each indefinite integral. 6x2(2x3+7)32dx
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Evaluate the following integral, where R is bounded by x = 1, y = 2x + 4, and y = -x-2. SS² dA R
Transcribed Image Text:Evaluate the following integral, where R is bounded by x = 1, y = 2x + 4, and y = -x-2. SS² dA R
RIVE *SF* off R ² dA ; [(x = 11₁ y = 2 + +4₁ y=-x-2 -2 x² dydx 31 उँ dx →→ [ (2x+4)³ 3 uzy4) du = dx 2x+y=-x-2 3x+4= -2 3x = -6 x=-21 [10²] 3 41 41 1 + [ 2² ( x + 2)² = (-1Xx +²2) ²] = √ 9 (x+3) dx h9 ([+]-[29X(+)₂ 5 1 (45) [1047-1975) (x+3) ² (x+3)³ dx => u (x+3) /9 1-2 u³ du = -2≤x≤1 -x-2 ≤ y ≤2x+4 = 191,25 = 765 h R @ AP
Transcribed Image Text:RIVE *SF* off R ² dA ; [(x = 11₁ y = 2 + +4₁ y=-x-2 -2 x² dydx 31 उँ dx →→ [ (2x+4)³ 3 uzy4) du = dx 2x+y=-x-2 3x+4= -2 3x = -6 x=-21 [10²] 3 41 41 1 + [ 2² ( x + 2)² = (-1Xx +²2) ²] = √ 9 (x+3) dx h9 ([+]-[29X(+)₂ 5 1 (45) [1047-1975) (x+3) ² (x+3)³ dx => u (x+3) /9 1-2 u³ du = -2≤x≤1 -x-2 ≤ y ≤2x+4 = 191,25 = 765 h R @ AP
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