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Chapter 6: Q. 3 (page 538)

What is the definition of the arc length of a continuous function fxon an interval a,b? Explain this definition in words in terms of a limit of sums, and explain the meaning of the notation used in the definition.

Short Answer

Expert verified

Arc length = limn鈫�鈭�鈭�k=1n1+鈭�yk鈭�x2鈭�x.

Step by step solution

01

Step 1. Given Information.

A continuous function fxon an interval a,b.

02

Step 2. Definition of arc length by limit of sum.

If the function is a differentiable and continuous derivative. Then the arc length of fxis given by

role="math" localid="1650561673811" limn鈫�鈭�鈭�k=1n1+鈭�yk鈭�x2鈭�x

Here, 鈭�x=b-an, xk=a+k鈭�x, 鈭�yk=f(xk)鈭�f(xk鈭�1)for allk=0,1,2....,n.

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