To determine Find the length of the curve x = cos t , y = t + sin t , 0 ≤ t ≤ π . Explanation Given data: x = cos t (1) y = t + sin t (2) Formula used: Consider the general formula for length for a ≤ t ≤ b . L = ∫ a b ( d x d t ) 2 + ( d y d t ) 2 d t (3) Calculation: Find d x d t Differentiate with respect to t of equation (1) as follows. d x d t = d d t [ cos t ] = − sin t Find d y d t Differentiate with respect to t of equation (2) as follows. d y d t = d d t ( t + sin t ) = d d t t + d d t sin t = 1 + cos t Substitute − sin t for d x d t and 1 + cos t for d y d t for 0 ≤ t ≤ π in equation (3) as follows. L = ∫ 0 π ( − sin t ) 2 + ( 1 + cos t ) 2 d t = ∫ 0 π sin 2 t + 1 + cos

University Calculus: Early Transcendentals, Loose-leaf Edition (4th Edition)

4th Edition

ISBN: 9780135164860

Author: Joel R. Hass, Christopher Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 10.2, Problem 25E

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Find the length of the curve x=cost, y=t+sint, 0≤t≤π.

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Chapter 10.2, Problem 24E

Chapter 10.2, Problem 26E

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Chapter 10 Solutions

University Calculus: Early Transcendentals, Loose-leaf Edition (4th Edition)

Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric...

Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Prob. 12E Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Prob. 14E Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric Equations...Ch. 10.1 - Finding Cartesian from Parametric...Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - In Exercises 19–24, match the parametric equations...Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - In Exercises 25–28, use the given graphs of x =...Ch. 10.1 - Finding Parametric Equations Find parametric...Ch. 10.1 - Find parametric equations and a parameter interval...Ch. 10.1 - Prob. 31E Ch. 10.1 - In Exercises 31–36, find a parametrization for the...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 - Prob. 44E Ch. 10.1 - Prob. 45E 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. 10.2 - In Exercises 1–14, find an equation for the line...Ch. 10.2 - In Exercises 1–14, find an equation for the line...Ch. 10.2 - In Exercises 1–14, find an equation for the line...Ch. 10.2 - In Exercises 1–14, find an equation for the line...Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - Prob. 7E Ch. 10.2 - Prob. 8E Ch. 10.2 - In Exercises 1–14, find an equation for the line...Ch. 10.2 - In Exercises 1–14, find an equation for the line...Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Prob. 15E Ch. 10.2 - Prob. 16E Ch. 10.2 - Prob. 17E Ch. 10.2 - Prob. 18E Ch. 10.2 - Prob. 19E Ch. 10.2 - Prob. 20E Ch. 10.2 - Prob. 21E Ch. 10.2 - Find the area enclosed by the y-axis and the...Ch. 10.2 - Prob. 23E Ch. 10.2 - Find the area under y = x3 over [0, 1] using the...Ch. 10.2 - Find the lengths of the curves in Exercises...Ch. 10.2 - Find the lengths of the curves in Exercises...Ch. 10.2 - Prob. 27E Ch. 10.2 - Prob. 28E Ch. 10.2 - Prob. 29E Ch. 10.2 - Prob. 30E Ch. 10.2 - Prob. 31E Ch. 10.2 - Find the areas of the surfaces generated by...Ch. 10.2 - Prob. 33E Ch. 10.2 - Prob. 34E Ch. 10.2 - Prob. 35E Ch. 10.2 - Prob. 36E Ch. 10.2 - Prob. 37E Ch. 10.2 - Find the coordinates of the centroid of the...Ch. 10.2 - Find the coordinates of the centroid of the...Ch. 10.2 - Prob. 40E Ch. 10.2 - Prob. 41E Ch. 10.2 - Prob. 42E Ch. 10.2 - Prob. 43E Ch. 10.2 - The curve with parametric equations is called a...Ch. 10.2 - Prob. 45E Ch. 10.2 - Prob. 46E Ch. 10.2 - Prob. 47E Ch. 10.2 - Volume Find the volume swept out by revolving the...Ch. 10.2 - Prob. 49E Ch. 10.2 - Prob. 50E Ch. 10.3 - Prob. 1E Ch. 10.3 - Prob. 2E Ch. 10.3 - Prob. 3E Ch. 10.3 - Prob. 4E Ch. 10.3 - Prob. 5E Ch. 10.3 - Prob. 6E Ch. 10.3 - Find the polar coordinates, 0 = ? = 2p and r = 0,...Ch. 10.3 - Prob. 8E Ch. 10.3 - Prob. 9E Ch. 10.3 - Find the polar coordinates, and , of the...Ch. 10.3 - Graph the sets of points whose polar coordinates...Ch. 10.3 - Prob. 12E Ch. 10.3 - Prob. 13E Ch. 10.3 - Prob. 14E Ch. 10.3 - Graph the sets of points whose polar coordinates...Ch. 10.3 - Prob. 16E Ch. 10.3 - Prob. 17E Ch. 10.3 - Prob. 18E Ch. 10.3 - Prob. 19E Ch. 10.3 - Prob. 20E Ch. 10.3 - Prob. 21E Ch. 10.3 - Prob. 22E Ch. 10.3 - Prob. 23E Ch. 10.3 - Prob. 24E Ch. 10.3 - Prob. 25E Ch. 10.3 - Prob. 26E Ch. 10.3 - Prob. 27E Ch. 10.3 - Prob. 28E Ch. 10.3 - Replace the polar equations in Exercises 2752 with...Ch. 10.3 - Prob. 30E Ch. 10.3 - Replace the polar equations in Exercises 2752 with...Ch. 10.3 - Prob. 32E Ch. 10.3 - Prob. 33E Ch. 10.3 - Prob. 34E Ch. 10.3 - Prob. 35E Ch. 10.3 - Prob. 36E Ch. 10.3 - Replace the polar equations in Exercises 27–52...Ch. 10.3 - Prob. 38E Ch. 10.3 - Prob. 39E Ch. 10.3 - Prob. 40E Ch. 10.3 - Prob. 41E Ch. 10.3 - Prob. 42E Ch. 10.3 - Prob. 43E Ch. 10.3 - Prob. 44E Ch. 10.3 - Prob. 45E Ch. 10.3 - Prob. 46E Ch. 10.3 - Replace the polar equations in Exercises 2752 with...Ch. 10.3 - Prob. 48E Ch. 10.3 - Prob. 49E Ch. 10.3 - Prob. 50E Ch. 10.3 - Prob. 51E Ch. 10.3 - Prob. 52E Ch. 10.3 - Replace the Cartesian equations in Exercises 5366...Ch. 10.3 - Prob. 54E Ch. 10.3 - Prob. 55E Ch. 10.3 - Prob. 56E Ch. 10.3 - Replace the Cartesian equations in Exercises 5366...Ch. 10.3 - Prob. 58E Ch. 10.3 - Replace the Cartesian equations in Exercises 53–66...Ch. 10.3 - Prob. 60E Ch. 10.3 - Prob. 61E Ch. 10.3 - Prob. 62E Ch. 10.3 - Prob. 63E Ch. 10.3 - Prob. 64E Ch. 10.3 - Prob. 65E Ch. 10.3 - Prob. 66E Ch. 10.3 - Prob. 67E Ch. 10.3 - Prob. 68E Ch. 10.4 - Prob. 1E Ch. 10.4 - Prob. 2E Ch. 10.4 - Prob. 3E Ch. 10.4 - Prob. 4E Ch. 10.4 - Prob. 5E Ch. 10.4 - Prob. 6E Ch. 10.4 - Prob. 7E Ch. 10.4 - Prob. 8E Ch. 10.4 - Prob. 9E Ch. 10.4 - Prob. 10E Ch. 10.4 - Prob. 11E Ch. 10.4 - Prob. 12E Ch. 10.4 - Prob. 13E Ch. 10.4 - Prob. 14E Ch. 10.4 - Prob. 15E Ch. 10.4 - Prob. 16E Ch. 10.4 - Find the slopes of the curves in Exercises 17-20...Ch. 10.4 - Find the slopes of the curves in Exercises 17-20...Ch. 10.4 - Find the slopes of the curves in Exercises 17-20...Ch. 10.4 - Find the slopes of the curves in Exercises 17-20...Ch. 10.4 - Prob. 21E Ch. 10.4 - Prob. 22E Ch. 10.4 - Prob. 23E Ch. 10.4 - Prob. 24E Ch. 10.4 - Prob. 25E Ch. 10.4 - Prob. 26E Ch. 10.4 - Prob. 27E Ch. 10.4 - Prob. 28E Ch. 10.4 - Prob. 29E Ch. 10.4 - Prob. 30E Ch. 10.4 - Prob. 31E Ch. 10.4 - Prob. 32E Ch. 10.4 - Prob. 33E Ch. 10.4 - Which of the following has the same graph as r =...Ch. 10.4 - Prob. 35E Ch. 10.4 - Prob. 36E Ch. 10.4 - Prob. 37E Ch. 10.4 - Prob. 38E Ch. 10.4 - Prob. 39E Ch. 10.4 - Prob. 40E Ch. 10.5 - Finding Polar Areas Find the areas of the regions...Ch. 10.5 - Finding Polar Areas Find the areas of the regions...Ch. 10.5 - Finding Polar Areas Find the areas of the regions...Ch. 10.5 - Finding Polar Areas Find the areas of the regions...Ch. 10.5 - Prob. 5E Ch. 10.5 - Prob. 6E Ch. 10.5 - Prob. 7E Ch. 10.5 - Prob. 8E Ch. 10.5 - Find the areas of the regions in Exercises...Ch. 10.5 - Find the areas of the regions in Exercises...Ch. 10.5 - Find the areas of the regions in Exercises...Ch. 10.5 - Prob. 12E Ch. 10.5 - Prob. 13E Ch. 10.5 - Prob. 14E Ch. 10.5 - Prob. 15E Ch. 10.5 - Prob. 16E Ch. 10.5 - Find the areas of the regions in Exercises...Ch. 10.5 - Find the areas of the regions in Exercises...Ch. 10.5 - Prob. 19E Ch. 10.5 - Prob. 20E Ch. 10.5 - Find the lengths of the curves in Exercises 2128....Ch. 10.5 - Prob. 22E Ch. 10.5 - Prob. 23E Ch. 10.5 - Prob. 24E Ch. 10.5 - Prob. 25E Ch. 10.5 - Prob. 26E Ch. 10.5 - Find the lengths of the curves in Exercises 2128....Ch. 10.5 - Prob. 28E Ch. 10.5 - Prob. 29E Ch. 10.5 - Prob. 30E Ch. 10.5 - Prob. 31E Ch. 10.5 - Prob. 32E Ch. 10 - Prob. 1GYR Ch. 10 - Prob. 2GYR Ch. 10 - Prob. 3GYR Ch. 10 - Prob. 4GYR Ch. 10 - Prob. 5GYR Ch. 10 - 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