   Chapter 10.2, Problem 43E

Chapter
Section
Textbook Problem

Find the exact length of the curve.43. x = t sin t, y = t cos t, 0 ≤ t ≤ 1

To determine

To find: the exact length of the curve for the parametric equation x=tsint and y=tcost.

Explanation

Given:

The parametric equation for the variable x is x=tsint.

The parametric equation for the variable y is y=tcost.

Formula used:

The length of the curve is obtained by the below formula.

L=αβ(dxdt)2+(dydt)2dt

Calculation:

Differentiate x=tsint the variable x with respect to t,

x=tsintdxdt=tcost+sint

Differentiate y=tcost the variable y with respect to t.

y=tcostdydt=tsint+cost

Use the above mentioned Formula and Substitute (tcost+sint) for dxdt, and (tsint+cost) for dydt in the above equation.

L=αβ(dxdt)2+(dydt)2dtL=01(tcost+sint)2+(tsint+cost)2dt=01t<

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Solve the equations in Exercises 112 for x (mentally, if possible). x3=1

Finite Mathematics and Applied Calculus (MindTap Course List)

Solve each equation: x8=6

Elementary Technical Mathematics

ex(ex)2 = a) ex3 b) e3x c) 3ex d) e4x

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Self Check Factor: 15a2+17a4.

College Algebra (MindTap Course List) 