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Chapter 6: Q. 31 (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=3x+1,a,b=-1,4

Short Answer

Expert verified

The arc length is510.

Step by step solution

01

Step 1. Given information .

Consider the given functionfx=3x+1.

02

Step 2. Formula used .

The formula used to find the arc length of the definite integral is ,

Arc length of fxfrom x=ato x=bisfx=鈭�ab1+f'x2dx

03

Step 3. Find the arc length .

fx=3x+1f'x=ddxfx=3

fx=鈭�ab1+f'x2dx=鈭�-141+32dx=鈭�-1410dx=10x-14=10路4+10路1=510

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