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5. Let C be the curve parameterized by r(t) = (t,-t,t²) Evaluate y ds.

5. Let C be the curve parameterized by r(t) = (t,-t,t²) Evaluate y ds.

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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5. Let \( C \) be the curve parameterized by \( \mathbf{r}(t) = \langle t, -t, t^2 \rangle \) with \( 0 \leq t \leq 1 \). Evaluate: \[ \int_{C} y \, ds. \] This problem involves evaluating a line integral along a curve \( C \) in a three-dimensional space, where the curve is given by the vector function \(\mathbf{r}(t)\). The parameter \(t\) ranges from 0 to 1. The integral specifically involves the \(y\)-component of the curve.
Transcribed Image Text:5. Let \( C \) be the curve parameterized by \( \mathbf{r}(t) = \langle t, -t, t^2 \rangle \) with \( 0 \leq t \leq 1 \). Evaluate: \[ \int_{C} y \, ds. \] This problem involves evaluating a line integral along a curve \( C \) in a three-dimensional space, where the curve is given by the vector function \(\mathbf{r}(t)\). The parameter \(t\) ranges from 0 to 1. The integral specifically involves the \(y\)-component of the curve.
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