Explanation Given: The Parametric equation for the variable x is as follows. x = 3 t 2 (1) The Parametric equation for the variable y is as follows. y = 2 t 3 (2) Calculation: Differentiate equation (1) with respect to t we get, d x d t = 6 t (3) Differentiate equation (2) with respect to t we get, d y d t = 6 t 2 (4) Length is determined for the limits of 0 to 2 . Calculate the length of the curve using the formula. L = ∫ 0 2 ( d x d t ) 2 + ( d y d t ) 2 d t (5) Substitute the expressions from equation (3) and (4) in equation (5). L = ∫ 0 2 ( d x d t ) 2 + ( d y d t ) 2 d t = ∫ 0 2 ( 6 t ) 2 + ( 6 t 2 ) 2 d t = ∫ 0 2 ( 36 t 2 + 36 t 4 ) d t = ∫ 0 2 36 t 2 ( 1 + t 2 ) d t = ∫ 0 2 6 t ( 1 + t 2 ) d t (6) To make the integration simple take u = ( 1 + t 2 ) (7) When the value of t = 0 , the value of u = 1

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Author: James Stewart

Publisher: Cengage Learning

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Chapter 10, Problem 37RE

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To find: the length of the curve x=3t2 and y=2t3 for 0≤t≤2 .

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Chapter 10, Problem 36RE

Chapter 10, Problem 38RE

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Chapter 10 Solutions

Single Variable Calculus

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Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Describe the motion of a particle with position...Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Match the parametric equations with the graphs...Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Use a graphing device and the result of Exercise...Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - Prob. 43E Ch. 10.1 - (a) Find parametric equations for the set of all...Ch. 10.1 - Suppose that the position of one particle at time...Ch. 10.1 - Prob. 46E Ch. 10.1 - Prob. 47E Ch. 10.1 - Prob. 48E Ch. 10.1 - Prob. 49E Ch. 10.1 - Prob. 50E Ch. 10.1 - Prob. 51E Ch. 10.1 - Prob. 52E Ch. 10.2 - Prob. 1E Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - Prob. 7E Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Find an equation of the tangent to the curve at...Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Find dy/dx and d2y/dx2. 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Use a graph to...Ch. 10.4 - Find the exact length of the curve. 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the length of the curve x = 3 t 2 and y = 2 t 3 for 0 ≤ t ≤ 2 .

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To find: the length of the curve x=3t2 and y=2t3 for 0≤t≤2 .

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Chapter 10 Solutions