Find the length of the curve.8(1) - (48, 1², 12³).r(t) =Osts 1

Given rt=4t,t2,16t3,0≤t≤1. The objective is to find the length of the curve. Formula Used : (1) The…

Answered: Find the length of the curve. 8(1) -…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Question

Find the length of the curve.
8(1) - (48, 1², 12³).
r(t) =
Osts 1

Expert Solution

Step 1

Given $r (t) = <4 t, t^{2}, \frac{1}{6} t^{3}>, 0 \leq t \leq 1$ .

The objective is to find the length of the curve.

Formula Used :

(1) The length of the curve $r (t)$ is $L = \int_{a}^{b} |r' (t)| d t$ .

(2) Power rule of differentiation is $\frac{d}{d x} (x^{n}) = n x^{n - 1}$ .

(3) The magnitude of the vector $|<a, b, c>| = \sqrt{a^{2} + b^{2} + c^{2}}$ .

(4) Power rule of integration is $\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + c$ where $c$ is the integrating constant.

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Find the length of the curve. 8(1) - (48, 1², 12³). r(t) = Osts 1