3. Consider the curve7 (t) = (1, t², „t³)Find the arc length from t = 0 to t = V5. Note: you might need "u-substitution"to finish evaluating the integral. 2. Consider the following vector-valued function7(t) = (t sint + cos t, sin t – t cos t, v6t?)|Compute the arc length from t = 0 to t = T.

Answered: 3. Consider the curve 7 (t) = (1, t²,…

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

3. Consider the curve
7 (t) = (1, t², „t³)
Find the arc length from t = 0 to t = V5. Note: you might need "u-substitution"
to finish evaluating the integral.

2. Consider the following vector-valued function
7(t) = (t sint + cos t, sin t – t cos t, v6t?)
|
Compute the arc length from t = 0 to t = T.

Expert Solution

Step 1

As we know that the expression of the arc length for the parametric curve is:

$L = \int_{t_{1}}^{t_{2}} \sqrt{{(\frac{d x}{d t})}^{2} + {(\frac{d y}{d t})}^{2} + {(\frac{d z}{d t})}^{2}} d t$

Given:

$\vec{r} (t) = <1, t^{2}, \frac{1}{3} t^{3}>$ & $t_{1} = 0, t_{2} = \sqrt{5}$

It means that:

$x = 1, y = t^{2}, z = \frac{1}{3} t^{2} N o w, \frac{d x}{d t} = \frac{d}{d t} (1) = 0 \frac{d y}{d t} = \frac{d}{d t} (t^{2}) = 2 t \frac{d z}{d t} = \frac{d}{d t} (\frac{t^{3}}{3}) = \frac{3 t^{2}}{3} = t^{2}$

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find the arc length of f(x) = In(sin(x)) for - 10 8
Find the definite integral of y=(1)/(x) on the interval [2, 3]. The approximate the arc length.
Find the exact length of the curve (x =t?cost ly=r?sint Osts2n 을 (T2 +4)3/2_4] a. l(m² + 43/2 – 1] (n² + 1)³/2 – 1] C. (n? + 4)3/2 – 1] d. 3/2 + е. a Ос e 이3 4|3 b.

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

3. Consider the curve 7 (t) = (1, t², *) Find the arc length from t = 0 to t = V5. Note: you might need "u-substitution" to finish evaluating the integral.