Let f (x, y, z) = x + yz and let C be the line segment from P = (0, 0, 0) to (8, 6, 6). (a) Calculate f (r (t)) and ds ||r' (t) || dt for the parameterization r(t) = (41², 312, 31²) for 0 < t ≤ √2. (Use symbolic notation and fractions where needed.) f(r (t)) = ds = (b) Evaluate f f (x, y, z) ds. (Use decimal notation. Give your answer to three decimal places.) [ f (x, y, z) ds = dt

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let f (x, y, z) = x + yz and let C be the line segment from P = (0,0,0) to (8, 6, 6).
(a) Calculate f (r (t)) and ds = ||r' (t) || dt for the parameterization r (t) = (4t², 3t², 3t²) for 0 ≤ t ≤ √√2.
(Use symbolic notation and fractions where needed.)
ƒ (r (t)) =
ds =
(b) Evaluate fe f (x, y, z) ds.
(Use decimal notation. Give your answer to three decimal places.)
[ (x, y, z) ds =
dt
Transcribed Image Text:Let f (x, y, z) = x + yz and let C be the line segment from P = (0,0,0) to (8, 6, 6). (a) Calculate f (r (t)) and ds = ||r' (t) || dt for the parameterization r (t) = (4t², 3t², 3t²) for 0 ≤ t ≤ √√2. (Use symbolic notation and fractions where needed.) ƒ (r (t)) = ds = (b) Evaluate fe f (x, y, z) ds. (Use decimal notation. Give your answer to three decimal places.) [ (x, y, z) ds = dt
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