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7. √√√1-2² Jo Jo Jo z sin x dy dz dx

7. √√√1-2² Jo Jo Jo z sin x dy dz dx

Calculus: Early Transcendentals
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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15.6 EXERCISES 1. Evaluate the integral in Example 1, integrating first with respect to y, then z, and then x. 2. Evaluate the integral fff (xy + z²) dV, where E = {(x, y, z) | 0 ≤ x ≤ 2,0 ≤ y ≤ 1,0 ≤z <3} using three different orders of integration. 3-8 Evaluate the iterated integral. Cy-z 3. f²f²f²* (2x - y) dx dy dz Jo Jo Jo 4. 4 6. (x+y 8. Jy Jo In x 5. 1² 12² * xe dy dx dz 10 6xy dz dx dy CC™ √1-2² Z y + 1 dx dz dy 7. z sin x dy dz dx Jo Jo 3²-²-²xye² dz dy dx W 32-28 apvig 111 111** shivic 9-18 Evaluate the triple integral. 9. SSSE y dv, where E = {(x, y, z) | 0 ≤ x ≤ 3,0 ≤ y ≤ x₂ x - y ≤z<x+y} 10. SSS e/ydV, where E = {(x, y, z) | 0 ≤ y ≤ 1, y ≤x≤ 1,0 ≤z<xy} 4V, where ܕܨ ܢ ܕܨ jffk .11 3) bdw 8 SSSE Z x² + z² V6 ( E = {(x, y, z) | 1 ≤ y ≤ 4, y ≤z ≤ 4,0≤x≤z} 12. SSS sin y dV, where E lies below the plane z = x and above the triangular region with vertices (0, 0, 0), (7, 0, 0), and (0, TT, 0) 13. SS 6xy dV, where E lies under the plane z = 1+x+y and above the region in the xy-plane bounded by the curves y = √√√x, y = 0, and x = 1 14. fff (x - y) dv, where E is enclosed by the surfaces z = x² = 1, z = 1 = x², y = 0, and y = 2 15. ry² dv, where T is the solid tetrahedron with vertices (0, 0, 0), (2, 0, 0), (0, 2, 0), and (0, 0, 2)
Transcribed Image Text:15.6 EXERCISES 1. Evaluate the integral in Example 1, integrating first with respect to y, then z, and then x. 2. Evaluate the integral fff (xy + z²) dV, where E = {(x, y, z) | 0 ≤ x ≤ 2,0 ≤ y ≤ 1,0 ≤z <3} using three different orders of integration. 3-8 Evaluate the iterated integral. Cy-z 3. f²f²f²* (2x - y) dx dy dz Jo Jo Jo 4. 4 6. (x+y 8. Jy Jo In x 5. 1² 12² * xe dy dx dz 10 6xy dz dx dy CC™ √1-2² Z y + 1 dx dz dy 7. z sin x dy dz dx Jo Jo 3²-²-²xye² dz dy dx W 32-28 apvig 111 111** shivic 9-18 Evaluate the triple integral. 9. SSSE y dv, where E = {(x, y, z) | 0 ≤ x ≤ 3,0 ≤ y ≤ x₂ x - y ≤z<x+y} 10. SSS e/ydV, where E = {(x, y, z) | 0 ≤ y ≤ 1, y ≤x≤ 1,0 ≤z<xy} 4V, where ܕܨ ܢ ܕܨ jffk .11 3) bdw 8 SSSE Z x² + z² V6 ( E = {(x, y, z) | 1 ≤ y ≤ 4, y ≤z ≤ 4,0≤x≤z} 12. SSS sin y dV, where E lies below the plane z = x and above the triangular region with vertices (0, 0, 0), (7, 0, 0), and (0, TT, 0) 13. SS 6xy dV, where E lies under the plane z = 1+x+y and above the region in the xy-plane bounded by the curves y = √√√x, y = 0, and x = 1 14. fff (x - y) dv, where E is enclosed by the surfaces z = x² = 1, z = 1 = x², y = 0, and y = 2 15. ry² dv, where T is the solid tetrahedron with vertices (0, 0, 0), (2, 0, 0), (0, 2, 0), and (0, 0, 2)
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