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Question

# Determine which value best approximates the arc length represented by the integral. Make your selection on the basis of a sketch of the arc, not by performing calculations.$\int_0^2 \sqrt{1+\left[\frac{d}{d x}\left(\frac{5}{x^2+1}\right)\right]^2} d x$$\text{value} = 7$

Solution

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This exercise aims to determine whether $7$ represents the best approximation of the arc length represented by the following integral:

$\int_0^2\sqrt{1+\left[\dv{}{x}\left(\dfrac{5}{1+x^2}\right)\right]^2}\mathrm dx.$

So, we need to determine the arc length of the function $f(x)=\dfrac{5}{x^2+1}$ from $0$ to $2$ based on the graph.

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