Consider the following parametric surface (u, v) E R S: r(u, v) = ui + vj + (1 + u – v)k, where Ris the region {(u, v)| 0 < u <1, 0 < v < 1 – u} in the uo-plane. The components a, b and c of T, X r, = ai + bj + ck are integers in this case. Enter these values below. Do not use decimal points. Hence evaluate the surface integral of the vector field F(z, y, z) = y'i+ 2j- rk over the surface S F.ndS Enter your answer using two decimal places.

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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Consider the following parametric surface
S: r(u, v) = ui + vj + (1 + u – v)k, (u, v) E R
where Ris the region {(u, v)| 0 < u <1, 0 < v <1 – u} in the uo-plane.
The components a, b and c of
T, × r, = ai + bj + ck
are integers in this case. Enter these values below. Do not use decimal points.
a =
Hence evaluate the surface integral of the vector field F(r, y, 2)=y'i+2j- zk over the surface S.
F.ndS
Enter your answer using two decimal places.
Transcribed Image Text:Consider the following parametric surface S: r(u, v) = ui + vj + (1 + u – v)k, (u, v) E R where Ris the region {(u, v)| 0 < u <1, 0 < v <1 – u} in the uo-plane. The components a, b and c of T, × r, = ai + bj + ck are integers in this case. Enter these values below. Do not use decimal points. a = Hence evaluate the surface integral of the vector field F(r, y, 2)=y'i+2j- zk over the surface S. F.ndS Enter your answer using two decimal places.
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