Ils z² ds, worlas-1- S is the part of the paraboloid x = y² + z² given by 0≤x≤1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
16.7
13 Evaluate the surtace
![6. Js xyz ds,
S is the cone with parametric equations x = u cos v,
u, 0≤u≤ 1,0 ≤v≤ π/2
y = u sin v, z =
=
7. sy ds, S is the helicoid with vector equation
= (u cos v, u sin v, v), 0≤ u≤ 1,0 ≤v≤ T
8. ffs (x² + y²) ds,
S is the surface with vector equation e
r(u, v) = (2uv, u² - v², u² + v²), u² + v² ≤ 1
9. ff, x²yz ds, is
od 111
EA
S is the part of the plane z = 1+ 2x + 3y that lies above
the rectangle [0, 3] × [0, 2]
thing
10. ff, xz ds,
S is the part of the plane 2x + 2y + z = 4 that lies in the
TOR
first octant
11. ffs x ds,
S is the triangular region with vertices (1, 0, 0), (0, -2, 0),
and (0, 0, 4)
CUST
220158 woll 185d to steach bel
so t
ad 38 70302
12. ffs y ds,
S is the surface z = (x³/2 + y³/2), 0≤x≤ 1,0 ≤ y ≤1
13. ff, z² ds, world
orga
12 als + 1k
S is the part of the paraboloid x = y² + z² given by
0≤x≤ 1
14. sy²z² ds,
S is the part of the cone y = √√x² + z² given by 0 ≤ y ≤5
15. , x ds,
S is the surface y = x² + 4z, 0≤x≤ 1,0 ≤ z≤1
16. ffs y² ds, la noinsy,
S is the part of the sphere x² + y² + z² = 1 that lies above
the cone z =
= √√√x² + y²
w) 2 to ovill
17. fjs (x²z + y²z) ds,
S is the hemisphere x² + y² + z² = 4, z = 0
S is the part of the half-cylinder x² + z² = 1, z>0, that
18. ffs (x + y + z) dS,
SE
22. F(x, y, z) = zi +
S is the helicoid
23. F(x, y, z)=xy i
paraboloid z = .
0≤x≤ 1,0 ≤
24. F(x, y, z) = -x
z = √√√x² + y²
downward orie:
25. F(x, y, z) = xi
and center the
26. F(x, y, z) = y
x² + y² + z²
27. F(x, y, z) = y
S consists of t
and the disk x
28. F(x, y, z)= y
S is the surfa
upward orier
29. F(x, y, z) =
S is the cube
30. F(x, y, z) =
region enclo
y = 0 and x
31. F(x, y, z)=
solid half-c
32. F(x, y, z) =
S is the sur
(1, 0, 0), (C
CAS 33. Evaluate
mal places
0≤y≤
CAS 34. Find the e
z = x²y²
CAS 35. Find the
mal place](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1be8149a-7f70-4e17-bee2-140ac0078ae6%2Fbdc70293-6d00-489a-b1dc-4ad87974d8f9%2Fbhch9c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Js xyz ds,
S is the cone with parametric equations x = u cos v,
u, 0≤u≤ 1,0 ≤v≤ π/2
y = u sin v, z =
=
7. sy ds, S is the helicoid with vector equation
= (u cos v, u sin v, v), 0≤ u≤ 1,0 ≤v≤ T
8. ffs (x² + y²) ds,
S is the surface with vector equation e
r(u, v) = (2uv, u² - v², u² + v²), u² + v² ≤ 1
9. ff, x²yz ds, is
od 111
EA
S is the part of the plane z = 1+ 2x + 3y that lies above
the rectangle [0, 3] × [0, 2]
thing
10. ff, xz ds,
S is the part of the plane 2x + 2y + z = 4 that lies in the
TOR
first octant
11. ffs x ds,
S is the triangular region with vertices (1, 0, 0), (0, -2, 0),
and (0, 0, 4)
CUST
220158 woll 185d to steach bel
so t
ad 38 70302
12. ffs y ds,
S is the surface z = (x³/2 + y³/2), 0≤x≤ 1,0 ≤ y ≤1
13. ff, z² ds, world
orga
12 als + 1k
S is the part of the paraboloid x = y² + z² given by
0≤x≤ 1
14. sy²z² ds,
S is the part of the cone y = √√x² + z² given by 0 ≤ y ≤5
15. , x ds,
S is the surface y = x² + 4z, 0≤x≤ 1,0 ≤ z≤1
16. ffs y² ds, la noinsy,
S is the part of the sphere x² + y² + z² = 1 that lies above
the cone z =
= √√√x² + y²
w) 2 to ovill
17. fjs (x²z + y²z) ds,
S is the hemisphere x² + y² + z² = 4, z = 0
S is the part of the half-cylinder x² + z² = 1, z>0, that
18. ffs (x + y + z) dS,
SE
22. F(x, y, z) = zi +
S is the helicoid
23. F(x, y, z)=xy i
paraboloid z = .
0≤x≤ 1,0 ≤
24. F(x, y, z) = -x
z = √√√x² + y²
downward orie:
25. F(x, y, z) = xi
and center the
26. F(x, y, z) = y
x² + y² + z²
27. F(x, y, z) = y
S consists of t
and the disk x
28. F(x, y, z)= y
S is the surfa
upward orier
29. F(x, y, z) =
S is the cube
30. F(x, y, z) =
region enclo
y = 0 and x
31. F(x, y, z)=
solid half-c
32. F(x, y, z) =
S is the sur
(1, 0, 0), (C
CAS 33. Evaluate
mal places
0≤y≤
CAS 34. Find the e
z = x²y²
CAS 35. Find the
mal place
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