The graph of the equation x2/3+y1 = 51° is one of a family of curves called astroids because of their starlike appearance (as shown in the accompanying figure). Find the length of this particularastroid by finding the length of half the first-quadrant portion, y= (52/3 - x2/3)12 V2sx55, and multiplying by 8.

Given that the function is y=523-x2332,524≤x≤5. It is known that the arc length is given by…

Answered: The graph of the equation x2/3. +y3 =…

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

The graph of the equation x
2/3
+y1 = 51° is one of a family of curves called astroids because of their starlike appearance (as shown in the accompanying figure). Find the length of this particular
astroid by finding the length of half the first-quadrant portion, y= (52/3 - x2/3)12 V2
sx55, and multiplying by 8.

Expert Solution

Step 1

Given that the function is $y = {(5^{\frac{2}{3}} - x^{\frac{2}{3}})}^{\frac{3}{2}}, \frac{5 \sqrt{2}}{4} \leq x \leq 5$ .

It is known that the arc length is given by $L = \int_{a}^{b} \sqrt{1 + {(\frac{d y}{d x})}^{2}} d x$

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