The total curvature of the portion of a smooth curve that runs from s = so to s₁ >s can be found by integrating í from S1 t₁ t₁ • Sx/v/ dt, | |\ «- K ds = SK So so to s₁. If the curve has some other parameter, say t, then the total curvature is K = where to and t₁ correspond to so and s₁. a. Find the total curvature of the portion of the helix r(t) = ( cos t)i + ( sin t)j + tk, 0≤t≤4r. b. Find the total curvature of the parabola y = v = 10x², – -∞
The total curvature of the portion of a smooth curve that runs from s = so to s₁ >s can be found by integrating í from S1 t₁ t₁ • Sx/v/ dt, | |\ «- K ds = SK So so to s₁. If the curve has some other parameter, say t, then the total curvature is K = where to and t₁ correspond to so and s₁. a. Find the total curvature of the portion of the helix r(t) = ( cos t)i + ( sin t)j + tk, 0≤t≤4r. b. Find the total curvature of the parabola y = v = 10x², – -∞
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 33E
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning