repeat-exercise-29-for-the-curve-y-x-sin-x-0-le-x-le-2pi

Question

Repeat Exercise 29 for the curve
$ y = x + \sin x $               $ 0 \le x \le 2\pi $

Clarissa Noh · Accepted Answer

he has clear Is that when you raid here? So for part A, we&#x27;re gonna draw a graph and I look something like this for part B. We&#x27;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&#x27;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&#x27;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&#x27;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&#x27;re using, um, straight lines.

Problem

Use either a computer algebra system or a table o…

Problem 30 Hard Difficulty

Repeat Exercise 29 for the curve
$ y = x + \sin x $ $ 0 \le x \le 2\pi $

Answer

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) $L \approx 9.50759$

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Video Transcript

Calculus: Early Transcendentals

Grace H.

Catherine R.

Heather Z.

Kayleah T.

Integration Review - Intro

Definite vs Indefinite

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) $L \approx 9.50759$

Calculus: Early Transcendentals

Grace H.

Catherine R.

Heather Z.

Kayleah T.

Integration Review - Intro

Definite vs Indefinite

Grace H.

Catherine R.

Heather Z.

Kayleah T.

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) $L \approx 9.50759$