Chapter 6: Q. 32 (page 539)

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.
$f (x) = 4 - x$ , $[a, b] = [2, 5]$

Short Answer

Expert verified

The arc length is $3 \sqrt{2}$ .

Step by step solution

Step 1. Given information .

Consider the given function $f (x) = 4 - x$ .

Step 2. Formula used .

The formula used to find the arc length from $x = a$ to $x = b$ is ,

Arc length oflocalid="1649150288054" $f (x) = \int_{a}^{b} \sqrt{1 + {(f' (x))}^{2}} d x$ .

Step 3. Find the arc length .

$f (x) = 4 - x f' (x) = \frac{d}{d x} [f (x)] = - 1$

$A r c l e n g t h = \int_{2}^{5} \sqrt{1 + {(- 1)}^{2}} d x = {[\sqrt{2} x]}_{2}^{5} = [\sqrt{2} \cdot 5 - \sqrt{2} \cdot 2] = 5 \sqrt{2} - 2 \sqrt{2} = 3 \sqrt{2}$

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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.
$f (x) = 4 - x$ , $[a, b] = [2, 5]$

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Formula used .

Step 3. Find the arc length .

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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.fx=4-x ,a,b=2,5

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Formula used .

Step 3. Find the arc length .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Theoretical and Mathematical Physics

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Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

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.
$f (x) = 4 - x$ , $[a, b] = [2, 5]$