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Midpoint Rule of rectangles

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Using rectangles whose height is given by the value of the function at the midpoint of the rectangles base (the midpoint rule); estimate the area under the graphs of the following functions, using first two and then four rectangles.

f(x)=8-x^2 between x=-4 and x=4.

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Midpoint Rule of rectangles is reiterated in the solution.

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Delta x = (b-a)/n = (4 -(-4))/4 = 2

Four intervals will be [-4, -2], [-2,0], ...

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Sandhya Sharma, MSc
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  • BSc, Meerut University
  • MSc, Meerut University
  • MPhil, Institute of Advanced Studies
  • MSc, AIT
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