Chapter 8.1, Problem 35E

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

Chapter
Section

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

# Find the arc length function for the curve y = 2x3/2 with starting point P0(1, 2).

To determine

To find: The arc length for the curve y=2x32.

Explanation

Given information:

The curve function is y=f(x)=2x32 (1)

The lower limit is 1.

The expression to find the arc length of the curve s(x) is shown below:

s(x)=âˆ«ax1+[f'(t)]2dt (2)

Here, the derivative of the function y with respect to t is f'(t) and the lower limit is a.

Differentiate Equation (1) with respect to x.

f'(x)=2(32)x32âˆ’1=3x12 (3)

Substitute t for x in Equation (3).

f'(t)=3t12

Substitute 3t12 for f'(t) and 1 for a in Equation (2).

L=âˆ«1x1+(3t12)2â€‰dt=âˆ«1x1+9tâ€‰dt=[

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