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The function is y=x2. As mentioned above the parameters are between x=a and x=b. Here a=0 and b=1.
The graph of the function-
y=xn where n=2.
The Area of the shaded region or area B was found to be 0.3333333333 units2.
Area A = 1- Area B
= 1- 0.33333333
= 0.6666666666 units2
Mathematically the area can also be found by the following-
Area A can be found by the formula- [pic]
Area B can be found by the formula- [pic]
Total Area = 1 unit2
Area B = [pic]
Area A = [pic]
Ratio of area A : area B
[pic] : [pic]
= 2 : 1(satisfies the conjecture n:1)
Now I will investigate the ratios of area A and B with other natural numbers...
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