aluate the line integral fc F dr, where F(x, y, z) =3 sin xi + 2 cos yj+ 4xzk and C is given by the vector nction r(t) = t'i – tj+t°k, 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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**Evaluate the Line Integral**

Evaluate the line integral \(\int_C \mathbf{F} \cdot d\mathbf{r}\), where \(\mathbf{F}(x, y, z) = 3 \sin x \, \mathbf{i} + 2 \cos y \, \mathbf{j} + 4xz \, \mathbf{k}\) and \(C\) is given by the vector function \(\mathbf{r}(t) = t^4 \mathbf{i} - t^3 \mathbf{j} + t^2 \mathbf{k}, \quad 0 \leq t \leq 1\).

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*Note: There is no graph or diagram associated with this problem.*
Transcribed Image Text:**Evaluate the Line Integral** Evaluate the line integral \(\int_C \mathbf{F} \cdot d\mathbf{r}\), where \(\mathbf{F}(x, y, z) = 3 \sin x \, \mathbf{i} + 2 \cos y \, \mathbf{j} + 4xz \, \mathbf{k}\) and \(C\) is given by the vector function \(\mathbf{r}(t) = t^4 \mathbf{i} - t^3 \mathbf{j} + t^2 \mathbf{k}, \quad 0 \leq t \leq 1\). --- *Note: There is no graph or diagram associated with this problem.*
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