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Numerade Educator

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Problem 24 Medium Difficulty

Graph the curve and visually estimate its length. Then use your calculator to find the length correct to four decimal places.

$ y = x + \cos x $ , $ 0 \le x \le \frac{\pi}{2} $

Answer

$L=\int_{0}^{\pi / 2} \sqrt{1+(1-\sin x)^{2}} d x \approx 1.7294$

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Video Transcript

he has clear suing you. Read here. So we hover formula Our equation minutes Why is equal to X was co sign and X is between zero and pi halves included. So we're going to graft first. It looks something like this on our derivative. We get a CZ one minus sign when we plug it into our length mark going Formula goes from zero to pie halves square root of one plus one minus sign squared d x When we calculated on the calculator they get around 1.7294