Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration

Q. 37

Found in: Page 499


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

Answers without the blur.

Just sign up for free and you're in.


Short Answer

Find the exact value of the arc length of each function f(x) on [a, b] by writing the arc length as a definite integral and then solving that integral.

f(x)=9-x2, a,b=-3,3

The arc length is 3π.

See the step by step solution

Step by Step Solution

Step 1. Given information. 

Consider the given function f(x)=9-x2, a,b=-3,3.

Step 2. Use arc length formula.

The formula for a function to find the arc length from x=a to x=b is given by role="math" localid="1649165845561" ab1+f'(x)2dx.

Step 3. Find the arc length. 

Arc length=-331+ddx9-x22dx=-331+129-x2-2x2dx=-331+-2x29-x22dx=-331+-x9-x22dx=-339-x2+x29-x2dx=-3399-x2dx=-3339-x2dx=3-π/2π/21du=3u-π/2π/2=3π2--π2=3π=3π

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.