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Chapter 6: Q. 38 (page 499)

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)=1-x2,a,b=-1,1

Short Answer

Expert verified

The arc length is蟺.

Step by step solution

01

Step 1. Given information. 

Consider the given function isf(x)=1-x2,a,b=-1,1.

02

Step 2. Use arc length formula.

The formula for a function to find the arc length from x=a to x=bis given by 鈭�ab1+f'(x)2dx.

03

Step 3. Find the arc length. 

Arclength=鈭�-111+ddx1-x22dx=鈭�-111+(-2x)21-x22dx=鈭�-111-x2+x21-x2dx=鈭�-1111-x2dx=arcsinx-11=arcsin(1)-arcsin(-1)=蟺2--蟺2=蟺

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