Math Portfolio- Shay Areas

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Dickerson 1

In order for one to understand, the process and subsequent work one must understand the purpose of this assignment, which is, to find a rule to approximate the area under the curve. Considering the following: g(x) = x2+3 (Ex 1)

Ex. 1

(Ex 2) allows one to see what area we are trying to find. The area is represented is represented by the green diagonals. This example is still from intervals x=0 to x=1.

Ex. 2

(Ex 3) shows us the estimation of the area by adding two trapezoids underneath the curve. One can observe that the area is not exact but still a good approximation. Using technology, I have found that the sums of the areas of both trapezoids are equal to 3.375. The next step will show one how to calculate this without the use of technology.

Ex. 3

To calculate the area one must know the formula for area of a trapezoid. The area of a trap is equal to the height (H) multiplied by the first base(b1) added to the second base(b2) divided by 2 represented by the formula (Ex 4):  

Ex. 4

As shown in (Ex 5) & (Ex 6) I will replace those variables for numbers that correspond to the two trapezoids seen in Ex 3.

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Ex. 5

   

As seen above I allowed:

b2=  3.25

b1=   3

H = .5

Once you substitute these numbers into the equation simple arithmetic will allow one to come to an answer

Thus, the area of the first trapezoid would be 1.5625.

                         

Ex. 6

Above I allowed:

b2=  4

b1=   3.25

H = .5

After substituting the variables for values, the equation should look like:

Thus, the Area of second trapezoid would be 1.81.

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