Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 8z) k C is the line segment from (2, 0, -1) to (4, 6, 3) (a) Find a function f such that F = Vf. f(x, y, z) = (b) Use part (a) to evaluate 1² F. dr along the given curve C.
Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 8z) k C is the line segment from (2, 0, -1) to (4, 6, 3) (a) Find a function f such that F = Vf. f(x, y, z) = (b) Use part (a) to evaluate 1² F. dr along the given curve C.
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 F and C below.**
\[
\mathbf{F}(x, y, z) = yz \, \mathbf{i} + xz \, \mathbf{j} + (xy + 8z) \, \mathbf{k}
\]
\( C \) is the line segment from \( (2, 0, -1) \) to \( (4, 6, 3) \).
**(a)** Find a function \( f \) such that \( \mathbf{F} = \nabla f \).
\( f(x, y, z) = \) [Text Box]
**(b)** Use part (a) to evaluate
\[
\int_C \mathbf{F} \cdot d\mathbf{r}
\]
along the given curve \( C \).
[Text Box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F481d8947-528e-477e-8558-b8f3bfa8246f%2Fb4a467f3-39da-49c0-9760-e095323508dd%2F1ixazi7_processed.png&w=3840&q=75)
Transcribed Image Text:**Consider F and C below.**
\[
\mathbf{F}(x, y, z) = yz \, \mathbf{i} + xz \, \mathbf{j} + (xy + 8z) \, \mathbf{k}
\]
\( C \) is the line segment from \( (2, 0, -1) \) to \( (4, 6, 3) \).
**(a)** Find a function \( f \) such that \( \mathbf{F} = \nabla f \).
\( f(x, y, z) = \) [Text Box]
**(b)** Use part (a) to evaluate
\[
\int_C \mathbf{F} \cdot d\mathbf{r}
\]
along the given curve \( C \).
[Text Box]
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