WEBVTT
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evaluate this integral using area. We could first graph
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the function the Inter grand there in green. And
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then we wanna look at the area under the curve
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from negative or from 0 to 9. So obviously
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we have a lot more negative area than we have
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. Positive area. So there's going to be a
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negative and a girl here, Let's go ahead and
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find out exactly what the area of this triangle is
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. Andi, the base is going to be six
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because that's where it crosses the X axis and move
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that the the height is to so six times 2
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12 divided by 21 half base times height would get
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off an area here of positive six and then we
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want toe. Analyze the area here. But sorry
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, negative sex is what I meant. And then
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we wanna analyze the area for this triangle up top
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. Here it has a base of three and a
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height of one. So three times one divided by
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two would be three halves. So this has an
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area here of three halves, positive or negative or
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positive 1.5. So if we combine these now,
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we have negative sex below the X axis, so
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it's negative plus 1.5, and that would end up
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giving us the integral evaluates to negative 4.5. Or
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, of course, negative. Nine out is the
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same thing there as well, because that would end
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up evaluating to negative four and a half. So
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by splitting these up into triangles, using the area
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equals one half base times height and then identifying anything
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below the X axis is negative above. The X
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axis is positive, then that could be a way
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to combine these to find the area.