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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Let c be a smooth curve defined by r(t)= with 1
![Here is the transcribed text for an educational website:
---
**Problem:**
2. Let \( C \) be a smooth curve defined by the parametric equation \(\vec{r}(t) = \langle t, t^3 \rangle\) with \(1 \leq t \leq 2\). Find the length of the curve.
**Solution:**
To find the length of the curve \( C \), we use the formula for the arc length:
\[
L = \int_{C} ds
\]
This can be expressed as:
\[
L = \int_{1}^{2} |\vec{r}'(t)| \, dt
\]
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F778ebef2-39f8-4792-902a-c383666adfe6%2Fb7380355-6591-4d21-b468-84b03ea8cc1c%2F3wdxffb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Here is the transcribed text for an educational website:
---
**Problem:**
2. Let \( C \) be a smooth curve defined by the parametric equation \(\vec{r}(t) = \langle t, t^3 \rangle\) with \(1 \leq t \leq 2\). Find the length of the curve.
**Solution:**
To find the length of the curve \( C \), we use the formula for the arc length:
\[
L = \int_{C} ds
\]
This can be expressed as:
\[
L = \int_{1}^{2} |\vec{r}'(t)| \, dt
\]
---
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