anonymous
  • anonymous
Estimate the area under the graph of f(x) = 2 + 2x2 from x = -1 to x = 2 using three rectangles and right end-points
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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John_ES
  • John_ES
Well, we choose the height the rectangles to be, \[f(x) \Rightarrow x \text{ will be the middle point between the x partition }\] So, our x coordinates will be, \[x_1=(-1+0)/2=-0.5\]\[x_2=(1+0)/2=0.5\]\[x_3=(2+1)/2=1.5\] The base of each rectangle will have 1 unit of longitude, because, \[\text{(End point-First point)/(Number of rectangles)}(2-(-1))/3=1\] So the area will be, \[A\approx1\cdot(f(x_1)+f(x_2)+f(x_3))=11.5\]
anonymous
  • anonymous
why do you add 0 to -1 and 1 but add a 1 to 2 in order to find the coordinates ?
John_ES
  • John_ES
The idea is to find the middle point of the intervals, where the rectangle is possibly best placed.

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John_ES
  • John_ES
You can try other heights: left heights (-1,0,1) or right heights (0,1,2), but these sums are a worse aproximation.
John_ES
  • John_ES
You can check a graphic example here, http://demonstrations.wolfram.com/ComparingBasicNumericalIntegrationMethods/
anonymous
  • anonymous
Ahh! I see... ok thanks for your help

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