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3. Use the Fun.Theorem to evaluate F dr, where F = 3xy?ī+ 3x*yj , πί and C is the curve described by r(t) = (t + sin())i + (t + cos())j, 0

3. Use the Fun.Theorem to evaluate F dr, where F = 3xy?ī+ 3x*yj , πί and C is the curve described by r(t) = (t + sin())i + (t + cos())j, 0

Advanced Engineering Mathematics
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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3. Use the Fundamental Theorem of Line Integrals to evaluate \(\int_C \vec{F} \cdot d\vec{r}\), where \(\vec{F} = 3xy^2 \vec{i} + 3x^2y \vec{j}\) and \(C\) is the curve described by \(\vec{r}(t) = \left(t + \sin\left(\frac{\pi t}{2}\right)\right)\vec{i} + \left(t + \cos\left(\frac{\pi t}{2}\right)\right)\vec{j}\), \(0 \leq t \leq 1\).
Transcribed Image Text:3. Use the Fundamental Theorem of Line Integrals to evaluate \(\int_C \vec{F} \cdot d\vec{r}\), where \(\vec{F} = 3xy^2 \vec{i} + 3x^2y \vec{j}\) and \(C\) is the curve described by \(\vec{r}(t) = \left(t + \sin\left(\frac{\pi t}{2}\right)\right)\vec{i} + \left(t + \cos\left(\frac{\pi t}{2}\right)\right)\vec{j}\), \(0 \leq t \leq 1\).
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