This question was asked before, but I'm being told its incorrect. Can I get someone else to answer this? **Problem Statement:**Find the exact length of the curve for the given function.**Function:**\[ y = 1 + 8x^{3/2} \]**Interval:**\[ 0 \leq x \leq 1 \]**Solution Approach:**To find the exact length of the curve, we will use the arc length formula for a curve defined by $ y = f(x) $ on the interval $[a, b]$:\[ L = \int_{a}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx \]1. **Differentiate the Function:** Find the derivative $\frac{dy}{dx}$ of the given function $ y = 1 + 8x^{3/2} $.2. **Set Up the Integral:** Substitute the derivative into the arc length formula and calculate the integral: \[ L = \int_{0}^{1} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx \]This approach will yield the exact length of the curve from $ x = 0 $ to $ x = 1 $.

Answered: Find the exact length of the curve. y =…

Math

Calculus

Find the exact length of the curve. y = 1 + 8x3/2, 0sxs1

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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Question

This question was asked before, but I'm being told its incorrect. Can I get someone else to answer this?

**Problem Statement:**

Find the exact length of the curve for the given function.

**Function:**

\[ y = 1 + 8x^{3/2} \]

**Interval:**

\[ 0 \leq x \leq 1 \]

**Solution Approach:**

To find the exact length of the curve, we will use the arc length formula for a curve defined by $ y = f(x) $ on the interval $[a, b]$:

\[ L = \int_{a}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx \]

1. **Differentiate the Function:**

Find the derivative $\frac{dy}{dx}$ of the given function $ y = 1 + 8x^{3/2} $.

2. **Set Up the Integral:**

Substitute the derivative into the arc length formula and calculate the integral:

\[ L = \int_{0}^{1} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx \]

This approach will yield the exact length of the curve from $ x = 0 $ to $ x = 1 $.

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