Calculate the surface integral where S is the portion of the plane lying in the first octant (x ≥ 0, y ≥ 0, z ≥ 0). f (x + y + 2)ds, S x + 2y + 4z = 4

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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I thought a step is wrong, equation should times 4 not 1/4, so it would be square root of 21 times equation. I need to check my answer, if I am wrong please tell me why, thanks.

Calculate the surface integral
where S is the portion of the plane
lying in the first octant (x ≥ 0, y ≥ 0, z ≥ 0).
ff (x+y+z)dS,
x + 2y + 4z = 4
Transcribed Image Text:Calculate the surface integral where S is the portion of the plane lying in the first octant (x ≥ 0, y ≥ 0, z ≥ 0). ff (x+y+z)dS, x + 2y + 4z = 4
2
4-2y
3x
I
=
- ✓ ] [ ] ² (² ² + 2
√21
4
4
0
+ 1)dx]dy =
2
4-2y
√ [] | []
16
(3x +2y+4) dx dy
Transcribed Image Text:2 4-2y 3x I = - ✓ ] [ ] ² (² ² + 2 √21 4 4 0 + 1)dx]dy = 2 4-2y √ [] | [] 16 (3x +2y+4) dx dy
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