Substitute these partial derivatives into √√1 + [9x(x, y)]²+ [g,(x, y)]². X ✓ 1 + [9x (x, y)]²+ [gy (x, y)]² ² + y ² ) ² + ( √²2² +2 1+ 1+ 2/1 +² + X
Substitute these partial derivatives into √√1 + [9x(x, y)]²+ [g,(x, y)]². X ✓ 1 + [9x (x, y)]²+ [gy (x, y)]² ² + y ² ) ² + ( √²2² +2 1+ 1+ 2/1 +² + X
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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Question
15.6-9 Please help
![eff RX₁
Evaluate
f(x, y, z) ds.
f(x, y, z)=√√√x² + y² + z²
S: z = √√√x² + y², (x - 1)² + y² ≤ 1
Part 1 of 6
Find the surface integral using the formula
JJ, RX,
s=1/₂"
f(x, y, g(x, y))√1 + [gx (x, y)]²+ [gy (x, y)]² da.
JR
Here, g(x, y) = Z = √x² + y². Find the partial derivatives gx(x, y) and gy(x, y).
f(x, y, z) ds
9x(x, y) =
gy(x, y) =
X
+
y
√x² + y²
Part 2 of 6
Substitute these partial derivatives into ✓1+ [gx(x, y)]²+ [gy(x, y)]².
1 + [gx (x, y)]²+ [gy (x, y)]²
=
=
1 +
=
y²
-X²2 + +
x² + y² x² + y²
1 +
= V1 +
(√x ² + √² ) ². + (√x ² + y ² ) ²
x² +
V1 +
2/1
x² + y²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F869ece4c-a274-4216-a84b-f797770a414f%2F77d9ec3e-8fbc-4278-9e1b-cdfad711b099%2Fa0f4yin_processed.png&w=3840&q=75)
Transcribed Image Text:eff RX₁
Evaluate
f(x, y, z) ds.
f(x, y, z)=√√√x² + y² + z²
S: z = √√√x² + y², (x - 1)² + y² ≤ 1
Part 1 of 6
Find the surface integral using the formula
JJ, RX,
s=1/₂"
f(x, y, g(x, y))√1 + [gx (x, y)]²+ [gy (x, y)]² da.
JR
Here, g(x, y) = Z = √x² + y². Find the partial derivatives gx(x, y) and gy(x, y).
f(x, y, z) ds
9x(x, y) =
gy(x, y) =
X
+
y
√x² + y²
Part 2 of 6
Substitute these partial derivatives into ✓1+ [gx(x, y)]²+ [gy(x, y)]².
1 + [gx (x, y)]²+ [gy (x, y)]²
=
=
1 +
=
y²
-X²2 + +
x² + y² x² + y²
1 +
= V1 +
(√x ² + √² ) ². + (√x ² + y ² ) ²
x² +
V1 +
2/1
x² + y²
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