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Repeat Exercise 29 for the curve

$ y = x + \sin x $ $ 0 \le x \le 2\pi $

a) Graph for the curve $y=x+\sin x, 0 \leq x \leq 2 \pi$ is shown below $:$

b) $\sqrt{1+(\sqrt[3]{3})^{2}}+\sqrt{\left(1+(2 \sqrt[3]{2}-\sqrt[3]{3})^{2}\right.}+\sqrt{1+(3-2 \sqrt[3]{2})^{2}}+\sqrt{1+9} \approx 7.5$

c) $L=\int_{0}^{2 \pi} \sqrt{1+(1+\cos x)^{2}} d x$

d) $L \approx 9.50759$

Applications of Integration

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Missouri State University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

he has clear Is that when you raid here? So for part A, we're gonna draw a graph and I look something like this for part B. We're finding the length of the curves so from zero calmer of zero and to pie comma f of two pi This is equal to two pi common to pine So the lanes is around Beat 0.9 when we're finding for the polygon of zero comma zero Hi, comma half of pine This is equal Thio Pikom a pie and two pi comma to pie So this also gives us around 8.9 We're finding for the polygon with four sides So zero comma zero I have a comma one plus I haves Pikom a pie three pi house comma three pie hands minus one and two pi comma to pie Then we get around 9.4 for part C We're gonna find the Ark links equation So when we derive our function why is equal to X plus sign? We get one plus co sign so are are killing Equation goes from 0 to 2 pi square root of one plus one plus co sign squared D X and for party. This gives us around nine points. 507 59 And for part B, our approximation was less than our actual since we're using, um, straight lines.