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.)

021+[ddx(5x2+1)]2dx\displaystyle\int_0^2\sqrt{1+\left[\frac{d}{d x}\left(\frac{5}{x^2+1}\right)\right]^2} d x



Answered 1 year ago
Answered 1 year ago
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The given function is: f(x)=5x2+1f(x)=\frac{5}{x^2+1} 'slader' Since the area of integration is: 0<x<20<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.

s4s\approx4 \\

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

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