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For the following exercises, use a calculator to draw the region, then compute the center of mass $(\overline{x}, \overline{y}) .$ Use symmetry to help locate the center of mass whenever possible.The region bounded by $\quad y=\cos (2 x)$ $x=-\frac{\pi}{4}, \quad$ and $x=\frac{\pi}{4}$

$\left(0, \frac{\pi}{8}\right)$

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 6

Moments and Centers of Mass

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since no density Funston is given. So we will assume that the reason has a uniform. Dante, that is density is the constant not from the figure. This is the figure we can see. The boundaries off X exists. The morning is is minus by a four by four way See that the reason has symmetry with respect due y axis This symmetry so like this. So this is the symmetry. This line divides the two part of the graph this rentable order. So this is the symmetry to Texas now on DDE hence ex body questioned you. Therefore we needed to calculate Why won't one Lee since we is you? That the reason hat uniform density Therefore come on, My bar equals one upon toe into you'll off. It will be affects. Sorry, Whole Esquire dicks Ban here, Toby. Offensive deice equal This when about to integer off. Minus pirate fool to find four causes Squad Rex digs a bomb you do love minus by by four you buy my food because two ex index So this is eagle do 112 integral off minus by. Wherefore by a pawn forward, huh? Cause for X plus one dicks a band didn't love minus two by four to find by four cost to extend ears. Sins cost to Tita. Equus. Oh, sorry. Since cost of tea date was to costs for Tito minus one. Therefore, we have costs Party diapers cost duty dark plus one upon you. So we have this thing Aspirin, this formula. No, this is equal. Do when a born fool you jiggle off minus primal four by one Food. One less call for this DX about Sign to ex upon to minus pile one for toe by apart. Now this is equal do one of 14 x plus sign for ex upon four minus by upon for by a bond forth upon when I want to signed to X minus Bible for to buy a pawn four on this is equal Do one of one before. Why? Upon food last one upon food, A sign off according to buy a pawn for minus one upon four into minus pi upon for plus one upon four. Sign off for in tow, minus by upon forth. Bam! When I want to do in tow, Sign off. Doing two by four minus Sign off. Doing minus by 14 Eso This is equal to one of one Ford in tow by upon four plus Jiro minus one upon forward into minus pi upon for plus judo. When I want doing toe one minus off minus one. And so this is equal. Do fire upon 16 blessed by upon 16 upon. One. This is equal do to buy upon 16 equals by upon it. Therefore year center of mass As it's about Inouye Vay, this is equal to do and by a point Sansa to the given problem.

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