   Chapter 8.1, Problem 23E

Chapter
Section
Textbook Problem

Graph the curve and visually estimate its length. Then use your calculator to find the length correct to four decimal places.23. y = x2 + x3, 1 ≤ x ≤ 2

To determine

To draw: The curve for the function y=x2+x3.

To find: The length of the curve.

Explanation

Given information:

The curve function is y=x2+x3 (1)

The lower limit is a=1 and the upper limit is b=2.

Calculation:

Draw the graph for the function y=x2+x3 as shown in Figure 1.

Refer Figure 1.

The length of the curve is slightly larger than the hypotenuse of the triangle.

The triangle is formed by the coordination points (1,2), (1,12), and (2,12).

Calculate the length of the hypotenuse as follows:

102+1210

Therefore, the length of the curve from graph is 10

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