Let f(x, y) = x³ + y³. Consider the line segment from (0, 0) to (2, 2) using two different parametrizations: C1 : x = t, y =t, 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let f(x, y) = x³ + y³. Consider the line segment from (0, 0)
to (2, 2) using two different parametrizations:
C1 : x = t, y = t, 0 <t < 2
C2 : x = 2t, y = 2t, 0<t < 1
1. Calculate the line integral
So
L (z,
f(x, y) ds
[ Select ]
%3D
2. Compare the following two line integrals.
| f(x, y) ds [ Select ]
L f(2, y) ds
C2
Transcribed Image Text:Let f(x, y) = x³ + y³. Consider the line segment from (0, 0) to (2, 2) using two different parametrizations: C1 : x = t, y = t, 0 <t < 2 C2 : x = 2t, y = 2t, 0<t < 1 1. Calculate the line integral So L (z, f(x, y) ds [ Select ] %3D 2. Compare the following two line integrals. | f(x, y) ds [ Select ] L f(2, y) ds C2
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