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Use a graph to give a rough estimate of the area of the region that lies under the given curve. Then find the exact area.

$ y = 2 \sin x - \sin 2x $, $ 0 \le x \le \pi $

Area $=4$

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Missouri State University

University of Michigan - Ann Arbor

Idaho State University

okay. Using the gruff first, we show that this is our shaded region. Over here, we know this goes from 002 pi comma zero. Which means that if the area which square is 1/4 time's 1/4 which is 1/16 that we can calculate the area to be approximately the number of squares. So 60 two ish divide by 14 times 1/4 which is 1/16 which is like 3.9. Okay, let's calculate the exact area now. Zero pie. I noticed. These are our bounds on the graph top minus bottom. You know, the integral of sine X Executive Co Cenex. The two goes at the top. We pull out the two that's imprint the season. Make it 1/2 on the outside, the integral of Sinus coastline. This plugging in fundamental there of calculus. This gives us four. This is really close to 3.9