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Question

In this exercise, determine which value best approximates the length of the arc represented by the integral. (Make your selection on the basis of a sketch of the arc and not by performing any calculations.)

$\displaystyle\int_0^2\sqrt{1+\left[\frac{d}{d x}\left(\frac{5}{x^2+1}\right)\right]^2} d x$

$5$

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 2The given function is: $f(x)=\frac{5}{x^2+1}$ Since the area of integration is: $0<x<2$ the length cannot be smaller than 2. By looking at the graph and with the help of coordinate system we can approximate our length to 4 squares.

$s\approx4 \\$

In case b) the length is the closest to our approximate solution.
That is the **correct answer**.

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