.4) and C is parametrized by r(1) = (1,2,1?) for 0 < 1 < 1.8Compute . F· dr, where F(x, y) =z+1(Use symbolic notation and fractions where needed.)F. dr =

Given, F→(x, y, z)=8y3+1, 8z+1, 4 and C is parametrized by r→(t)=t3, 2, t2 for 0≤t≤1.

Answered: Compute ſ F · dr, where . dr,

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 32E

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Question

.4) and C is parametrized by r(1) = (1,2,1?) for 0 < 1 < 1.
8
Compute . F· dr, where F(x, y) =
z+1
(Use symbolic notation and fractions where needed.)
F. dr =

Expert Solution

Step 1

Given,

$\vec{F} (x, y, z) = <\frac{8}{y^{3} + 1}, \frac{8}{z + 1}, 4>$

and $C i s p a r a m e t r i z e d b y \vec{r} (t) = <t^{3}, 2, t^{2}> f o r 0 \leq t \leq 1 .$

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