Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base, estimate the area under the graph using first two and then four rectangles. f(x)equals=x squared2 between xequals=1 and xequals=2

The area under the graph by using the first two and then four rectangles is units square.

For reference use the below-given graph.

Given function is

 when to .

The first rectangle of the first part graph goes from to , so the width will be units. And the height measured from the middle point i.e. is

units.

Then the area of the first rectangle is units square.

Similarly, the second rectangle of the first part graph goes from to , so the width will be units. And the height measured from the middle point i.e.  is

units.

So, the area of the second rectangle is units square.

Hence, the final area under the graph will be units square.

Further, we can do the same for another part of the graph to find the area under the graph by using four rectangles.

For example,  the first rectangle of the four has a width of units and a height of

units.

Therefore, the area under the graph by using the first two and then four rectangles is units square.

Know more about the area under the curve here:

link

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step-by-step explanation: