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# Use Property 8 to estimate the value of the integral.$\displaystyle \int^{2\pi}_{\pi} (x - 2\sin x) \,dx$

## $\pi^{2} \leq \int_{\pi}^{2 \pi}(x-2 \sin x) d x \leq\left(\frac{5 \pi}{3}+\sqrt{3}\right)(\pi)$

Integrals

Integration

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

the first thing we can do is take the derivative, which is one minus to co sign acts we know F prime a vaccine. Other words. That derivative is equivalent to zero when Coastline X is 1/2 which happens a pile five pi over three. Therefore test the value of off of pie, which we get as high after five pi over three, which we get to be approximately 6.97 you know, pies approximately 3.14 and then lastly, off of two pi the complete circle with just 6.28 approximately 3.14 times two, which gives our expression so five pied over three plus word of three times pyre through Portland for

#### Topics

Integrals

Integration

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp