Chapter 9: Q. 2 (page 774)

The calculus of parametric equations: Let x = f(t) and y = g(t), where f and g are differentiable functions.
The arc length of the curve defined by the parametric equations on the interval [a, b] is . ....

Short Answer

Expert verified

The arc length is $\int_{a}^{b} \sqrt{{(f' (t))}^{2} + {(g' (t))}^{2}} d t$

Step by step solution

Step 1. Given information

The functions:

$x = f (t) y = g (t)$

$a \leq t \leq b$

Step 2. Arc length of the curve.

The arc length over given interval is:

$l = \int_{a}^{b} \sqrt{{(\frac{d x}{d t})}^{2} + {(\frac{d y}{d t})}^{2}} d t = \int_{a}^{b} \sqrt{{(f' (t))}^{2} + {(g' (t))}^{2}} d t$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

The calculus of parametric equations: Let x = f(t) and y = g(t), where f and g are differentiable functions.
The arc length of the curve defined by the parametric equations on the interval [a, b] is . ....

Short Answer

Step by step solution

Step 1. Given information

Step 2. Arc length of the curve.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Geometry

Discrete Mathematics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

The calculus of parametric equations: Let x = f(t) and y = g(t), where f and g are differentiable functions.The arc length of the curve defined by the parametric equations on the interval [a, b] is . ....

Short Answer

Step by step solution

Step 1. Given information

Step 2. Arc length of the curve.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Geometry

Discrete Mathematics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

The calculus of parametric equations: Let x = f(t) and y = g(t), where f and g are differentiable functions.
The arc length of the curve defined by the parametric equations on the interval [a, b] is . ....