Given the following vector field and orientated curve C, evaluate F.Tds. (x,y) F = on the curve r(t)= (2t,3t), for 1 sts2 The value of the line integral of F over C is (Type an exact answer, using radicals as needed.)
Given the following vector field and orientated curve C, evaluate F.Tds. (x,y) F = on the curve r(t)= (2t,3t), for 1 sts2 The value of the line integral of F over C is (Type an exact answer, using radicals as needed.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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![**Problem Statement:**
Given the following vector field and oriented curve \( C \), evaluate \( \int_C \mathbf{F} \cdot d\mathbf{s} \).
---
**Vector Field:**
\[
\mathbf{F} = \frac{\langle x, y \rangle}{(x^2 + y^2)^{3/2}}
\]
**Curve:**
\[
\mathbf{r}(t) = \langle 2t^2, 3t^2 \rangle, \quad \text{for } 1 \leq t \leq 2
\]
**Task:**
Find the value of the line integral of \( \mathbf{F} \) over \( C \).
**Note:**
(Type an exact answer, using radicals as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d940ce8-cba2-4a95-af25-aae0739ca5aa%2Fabace8eb-48f9-4fc2-b2c4-affb5baef2e2%2Fr2xbbb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given the following vector field and oriented curve \( C \), evaluate \( \int_C \mathbf{F} \cdot d\mathbf{s} \).
---
**Vector Field:**
\[
\mathbf{F} = \frac{\langle x, y \rangle}{(x^2 + y^2)^{3/2}}
\]
**Curve:**
\[
\mathbf{r}(t) = \langle 2t^2, 3t^2 \rangle, \quad \text{for } 1 \leq t \leq 2
\]
**Task:**
Find the value of the line integral of \( \mathbf{F} \) over \( C \).
**Note:**
(Type an exact answer, using radicals as needed.)
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