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Evaluate F ds (or F ds) where Jc F = (y – x2, z - y², x – z) and C is the curve r = joining (0,0,0) to (1,1,1). (t, t, t)

Evaluate F ds (or F ds) where Jc F = (y – x2, z - y², x – z) and C is the curve r = joining (0,0,0) to (1,1,1). (t, t, t)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem 11:** Evaluate \(\int_C \mathbf{F} \cdot d\mathbf{s}\) (or \(\oint_C \mathbf{F} \cdot d\mathbf{s}\)) where a) \(\mathbf{F} = (y-x^2, z-y^2, x-z^2)\) and \(C\) is the curve \(\mathbf{r} = (t, t, t^3)\) joining \((0,0,0)\) to \((1,1,1)\). **Explanation:** - The problem involves evaluating a line integral of a vector field \(\mathbf{F}\). - The vector field \(\mathbf{F}\) is given as a function of three components: \(y-x^2\), \(z-y^2\), and \(x-z^2\). - The curve \(C\) is parameterized by \(\mathbf{r} = (t, t, t^3)\), representing a path in three-dimensional space. - The integration limits go from \((0,0,0)\) when \(t=0\) to \((1,1,1)\) when \(t=1\).
Transcribed Image Text:**Problem 11:** Evaluate \(\int_C \mathbf{F} \cdot d\mathbf{s}\) (or \(\oint_C \mathbf{F} \cdot d\mathbf{s}\)) where a) \(\mathbf{F} = (y-x^2, z-y^2, x-z^2)\) and \(C\) is the curve \(\mathbf{r} = (t, t, t^3)\) joining \((0,0,0)\) to \((1,1,1)\). **Explanation:** - The problem involves evaluating a line integral of a vector field \(\mathbf{F}\). - The vector field \(\mathbf{F}\) is given as a function of three components: \(y-x^2\), \(z-y^2\), and \(x-z^2\). - The curve \(C\) is parameterized by \(\mathbf{r} = (t, t, t^3)\), representing a path in three-dimensional space. - The integration limits go from \((0,0,0)\) when \(t=0\) to \((1,1,1)\) when \(t=1\).
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