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2 Show that the total length of the astroid x¾ + y³ = a³, which can be parameterized as x = acos³0, y = asin³0, is 6a, where a is a nonzero constant. Hint: ds = (dx)² + (dy)² = √√/1 + (dy)²|dx|.

2 Show that the total length of the astroid x¾ + y³ = a³, which can be parameterized as x = acos³0, y = asin³0, is 6a, where a is a nonzero constant. Hint: ds = (dx)² + (dy)² = √√/1 + (dy)²|dx|.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 37E
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2 1. Show that the total length of the astroid x² + y² = a³, which can be parameterized as x = = acos³0, y = asin³0, is 6a, where a is a nonzero constant. Hint: ds = √(dx)² + (dy)² = √√1+ (dy)²|dx|.
Transcribed Image Text:2 1. Show that the total length of the astroid x² + y² = a³, which can be parameterized as x = = acos³0, y = asin³0, is 6a, where a is a nonzero constant. Hint: ds = √(dx)² + (dy)² = √√1+ (dy)²|dx|.
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