9. Find the surface area of the part of the cylinder y? + z2 = 9 that is above the rectangle R = [0,2] × [-3, 3].
9. Find the surface area of the part of the cylinder y? + z2 = 9 that is above the rectangle R = [0,2] × [-3, 3].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please do question 9
![Sea
1. Use a Riemann sum with m = 3 and n = 2 to estimate the value of
(x+ 2y) dA where
R
R= [0, 6] × [0, 2]. Take sample points to be the lower right corners.
-2
Compute /.
yev?
2.
dx dy.
+ x2
3. Compute
// 3ry? dy da.
4. Compute L
6xyz dz dr dy.
5. Compute
/ cos(y) dy dx by reversing the order of integration.
6. Find the volume of the solid bounded by the paraboloids z =
a? + y? and z = 2 – x2 - y?.
TY
7. Compute
dy dx by converting to polar coordinates.
VT2 + y?
4-12
8. Find the x-coordinate of the center of mass of the lamina that occupies the region D
{(x, y) | 0<x < 1, x² < y < 1} and has density function p(x, y) = x + y.
9. Find the surface area of the part of the cylinder y? + z2 = 9 that is above the rectangle
R = [0,2] × [-3, 3].
cln 4
cln 3
cln 2
10. Compute
e0.5x+y-z dz dy dx.
11. Find
/// ?y dV where E is the solid bounded by the cylinder y = x2 and the planes
z = 0, y = 1, and z = y.
%3D
12. Find the volume of the solid bounded by the cylinder x2 + y² = 4 and the planes z = 0 and
y + z = 3.
-2
4-y2
4-x2-y2
13. Compute
y? Vx2 + y2 + z2 dz dx dy by converting to spherical
4-22-y2
coordinates.
14. A sphere of radius k has a volume of Tk. Set up the iterated integrals in rectangular,
cylindrical, and spherical coordinates needed to compute this.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8781723f-cb28-44ac-b775-505bf5afefc1%2Fe0f31232-91de-44c0-a947-5de33a2603c3%2Fzpexgr7_processed.png&w=3840&q=75)
Transcribed Image Text:Sea
1. Use a Riemann sum with m = 3 and n = 2 to estimate the value of
(x+ 2y) dA where
R
R= [0, 6] × [0, 2]. Take sample points to be the lower right corners.
-2
Compute /.
yev?
2.
dx dy.
+ x2
3. Compute
// 3ry? dy da.
4. Compute L
6xyz dz dr dy.
5. Compute
/ cos(y) dy dx by reversing the order of integration.
6. Find the volume of the solid bounded by the paraboloids z =
a? + y? and z = 2 – x2 - y?.
TY
7. Compute
dy dx by converting to polar coordinates.
VT2 + y?
4-12
8. Find the x-coordinate of the center of mass of the lamina that occupies the region D
{(x, y) | 0<x < 1, x² < y < 1} and has density function p(x, y) = x + y.
9. Find the surface area of the part of the cylinder y? + z2 = 9 that is above the rectangle
R = [0,2] × [-3, 3].
cln 4
cln 3
cln 2
10. Compute
e0.5x+y-z dz dy dx.
11. Find
/// ?y dV where E is the solid bounded by the cylinder y = x2 and the planes
z = 0, y = 1, and z = y.
%3D
12. Find the volume of the solid bounded by the cylinder x2 + y² = 4 and the planes z = 0 and
y + z = 3.
-2
4-y2
4-x2-y2
13. Compute
y? Vx2 + y2 + z2 dz dx dy by converting to spherical
4-22-y2
coordinates.
14. A sphere of radius k has a volume of Tk. Set up the iterated integrals in rectangular,
cylindrical, and spherical coordinates needed to compute this.
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