Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Line Integral
A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along…
Triple Integral
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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 \(\mathbf{r}(t) = t^4 \mathbf{i} - t^3 \mathbf{j} + t^2 \mathbf{k}, \quad 0 \leq t \leq 1\). --- *Note: There is no graph or diagram associated with this problem.*
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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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