Find an estimate of the area under the graph of y= x^2 between x= 0 and x= 2 above the x-axis using four right endpoint rectangles.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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An estimate of the area under the graph of y= x^2 between x= 0 and x= 2 above the x-axis has to be determined using four right endpoint rectangles.

The approximate area is:

A = `0.5*(0.5^2 + 1^2 + 1.5^2 + 2^2)`

=> 0.5*(0.25 + 1 + 2.25 + 4)

=> 0.5*7.5

=> 3.75

The approximation of the area under the graph of y= x^2 between x= 0 and x= 2 above the x-axis using 4 right end-point rectangles is 3.75 square units.

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lfryerda's profile pic

lfryerda | High School Teacher | (Level 2) Educator

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To estimate the area from the graph of `y=x^2` and the x-axis and the lines `x=0` and `x=2`, we can use rectangles for the area.

Using four rectangles with the endpoints on the right means that we have the following rectangles:

`(0,0)` to `(0.5, 0)` to `(0.5, 0.5^2)` to `(0,0.5^2)`

`(0.5,0)` to `(1,0)` to `(1,1^2)` to `(0.5,1^2)`

`(1,0)` to `(1.5,0)` to `(1.5, 1.5^2)` to `(1,1.5^2)`

`(1.5,0)` to `(2,0)` to `(2,2^2)` to `(1.5,2^2)`

The rectangles have areas given by 0.125, 0.5, 1.125 and 2 repsectively, which means the approximation to the area under the curve is the sum of those numbers.

The estimate of the area under the curve is 3.75

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