Let S be the plane with equation 3x +9y+z= 4 in the first octant and which is in front of the zy-plane. We wish to evaluate the surface integral JJ's 10z³ds. The first step would be to parameterize the surface S. We will use the standard parameterization where z is a graph of z and y. Let z = z, y = y and z = 4 +-3 x+-9 y where (x, y) = D. We choose to express D as a Type 1 region. Then D = {(z,y) |0 ≤ 1 ≤ ,0≤y≤ Next, we calculate the partial derivatives of z with respect to and y, respectively. Finally, we can consider the surface integral: ffs 10z³ds = 102³ √GdA where G = + T}. Now all we need to do is evaluate the double integral on the right. After evaluation, we find the answer of the surface integral: ffs 10z³ds=
Let S be the plane with equation 3x +9y+z= 4 in the first octant and which is in front of the zy-plane. We wish to evaluate the surface integral JJ's 10z³ds. The first step would be to parameterize the surface S. We will use the standard parameterization where z is a graph of z and y. Let z = z, y = y and z = 4 +-3 x+-9 y where (x, y) = D. We choose to express D as a Type 1 region. Then D = {(z,y) |0 ≤ 1 ≤ ,0≤y≤ Next, we calculate the partial derivatives of z with respect to and y, respectively. Finally, we can consider the surface integral: ffs 10z³ds = 102³ √GdA where G = + T}. Now all we need to do is evaluate the double integral on the right. After evaluation, we find the answer of the surface integral: ffs 10z³ds=
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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![Let S be the plane with equation 3x +9y+z= 4 in the first octant and which is in front of the xy-plane. We wish to evaluate the surface integral
ffs 10z³ds.
The first step would be to parameterize the surface S. We will use the standard parameterization where z is a graph of and y.
Let z = z, y = y and z = 4
+-3
x+-9
y where (x, y) = D.
We choose to express D as a Type 1 region. Then
D = {(x, y) |0 ≤ x ≤
],0 ≤ y ≤
Next, we calculate the partial derivatives of z with respect to x and y, respectively.
||
Finally, we can consider the surface integral:
ffs 10r³ds=ffp 10z³√GdA
where G =
Now all we need to do is evaluate the double integral on the right. After evaluation, we find the answer of the surface integral:
ffs 10z³ds =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2b36003-ef33-455c-bcff-0e6c40acbd92%2Fd14c48b9-701f-4e49-af9a-2c3d04574856%2Fqz081tr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let S be the plane with equation 3x +9y+z= 4 in the first octant and which is in front of the xy-plane. We wish to evaluate the surface integral
ffs 10z³ds.
The first step would be to parameterize the surface S. We will use the standard parameterization where z is a graph of and y.
Let z = z, y = y and z = 4
+-3
x+-9
y where (x, y) = D.
We choose to express D as a Type 1 region. Then
D = {(x, y) |0 ≤ x ≤
],0 ≤ y ≤
Next, we calculate the partial derivatives of z with respect to x and y, respectively.
||
Finally, we can consider the surface integral:
ffs 10r³ds=ffp 10z³√GdA
where G =
Now all we need to do is evaluate the double integral on the right. After evaluation, we find the answer of the surface integral:
ffs 10z³ds =
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