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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.

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

Short Answer

Expert verified

The arc length is 32.

Step by step solution

01

Step 1. Given information .

Consider the given functionfx=4-x.

02

Step 2. Formula used .

The formula used to find the arc length from x=ato x=bis ,

Arc length oflocalid="1649150288054" fx=鈭�ab1+f'x2dx.

03

Step 3. Find the arc length .

fx=4-xf'x=ddxfx=-1

Arclength=鈭�251+-12dx=2x25=2路5-2路2=52-22=32

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