Set up an integral for the length of the curve. y=√₁-x²₁ - sxs ² 1/4 -1/4 5-4x4 4(1-x4) 1/4 -1/4 dx 1/4 1₁/41 4(1-x4) 1/4 4+16x6 4-4x4+16x6 dx 4-4x4+4x3 4(1-x4) dx dx
Set up an integral for the length of the curve. y=√₁-x²₁ - sxs ² 1/4 -1/4 5-4x4 4(1-x4) 1/4 -1/4 dx 1/4 1₁/41 4(1-x4) 1/4 4+16x6 4-4x4+16x6 dx 4-4x4+4x3 4(1-x4) dx dx
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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![**Set up an integral for the length of the curve.**
Given the function:
\[ y = \sqrt{1-x^4}, \quad -\frac{1}{4} \leq x \leq \frac{1}{4} \]
Select the correct integral that represents the length of the curve:
1. \[ \int_{-1/4}^{1/4} \sqrt{\frac{5 - 4x^4}{4(1-x^4)}} \, dx \]
2. \[ \int_{-1/4}^{1/4} \sqrt{\frac{4 - 4x^4 + 16x^6}{4(1-x^4)}} \, dx \]
3. \[ \int_{-1/4}^{1/4} \sqrt{\frac{4 + 16x^6}{4}} \, dx \]
4. \[ \int_{-1/4}^{1/4} \sqrt{\frac{4 - 4x^4 + 4x^3}{4(1-x^4)}} \, dx \]
Each integral is structured to determine the arc length of the given curve over the specified interval. Ensure to verify the correct integral setup.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8530ca5f-6e8e-4cce-aaa4-95b39b1a4e45%2F90c90775-9702-4875-9bee-18a04cf96253%2Fr26r3is_processed.png&w=3840&q=75)
Transcribed Image Text:**Set up an integral for the length of the curve.**
Given the function:
\[ y = \sqrt{1-x^4}, \quad -\frac{1}{4} \leq x \leq \frac{1}{4} \]
Select the correct integral that represents the length of the curve:
1. \[ \int_{-1/4}^{1/4} \sqrt{\frac{5 - 4x^4}{4(1-x^4)}} \, dx \]
2. \[ \int_{-1/4}^{1/4} \sqrt{\frac{4 - 4x^4 + 16x^6}{4(1-x^4)}} \, dx \]
3. \[ \int_{-1/4}^{1/4} \sqrt{\frac{4 + 16x^6}{4}} \, dx \]
4. \[ \int_{-1/4}^{1/4} \sqrt{\frac{4 - 4x^4 + 4x^3}{4(1-x^4)}} \, dx \]
Each integral is structured to determine the arc length of the given curve over the specified interval. Ensure to verify the correct integral setup.
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