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 Statement:**
Find the arc length of \( y = 2x^{3/2} \) on the interval \( 1 \leq x \leq 2 \).
**Solution:**
In this problem, we are asked to determine the arc length of the function \( y = 2x^{3/2} \) over the specified interval. To calculate the arc length of a function \( y = f(x) \) from \( x = a \) to \( x = b \), we use the formula:
\[
L = \int_{a}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx
\]
Let's find the derivative \(\frac{dy}{dx}\) and proceed with the computation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6cf09b2a-e92e-430b-8152-8153c73e6dd1%2F04817999-a440-426a-b548-60f58d924e82%2Fygbdln_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the arc length of \( y = 2x^{3/2} \) on the interval \( 1 \leq x \leq 2 \).
**Solution:**
In this problem, we are asked to determine the arc length of the function \( y = 2x^{3/2} \) over the specified interval. To calculate the arc length of a function \( y = f(x) \) from \( x = a \) to \( x = b \), we use the formula:
\[
L = \int_{a}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx
\]
Let's find the derivative \(\frac{dy}{dx}\) and proceed with the computation.
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