Math Ia Investigating Ratios of Areas and Volumes

Math HL Internal Assessment INVESTIGATING RATIOS OF AREAS AND VOLUMES The social function of this internal opinion is to investigate the ratios among the bea formed in a higher place and beneath a work of the type y=xn employ integrals. Integrals argon an essential part of calculus which lay offs us to make up the are of the region bounded by the function f(x) and the x or y axis, given a certain interval [a,b]. The promissory note used is shown down the stairs: This study allow for focus on leting a conjecture amidst the ratio of the eye socket above the mold (A) and the reach below the curve (B). A graph is shown below to illustrate A and B. To accomplish this, we will analyze several examples to extract a pattern and move up a conjecture, which will later on be proven. First of all, a study of the ratios for A and B will be conducted for the function y=x2, considering the region between x=0 to x=1 and the x-axis as the theatre of operations B, and the region between y=0 to y=1 and the y-axis the area A. 1. Function: y=x2 First of all, calculate and find the area under the curve (labeled B) from x=0 to x=1 Find A, by collusive the area of the substantive between the point (0,0), (0,1), (1,0) and (1,1) and then subtracting the area of B. The ratio of A to B in this case is 2.

employ the method in the example shown above, several functions of the type y=xn will be analyzed to determine whether there is a viable relationship between the ratios obtained and the initial function. In these setoff examples, n will only incl ude positive integers, n ? ?+ Example calc! ulations: Y=x1 Y=x3 Y=x4 Analysis of the way of functions of the type y=xn from x=0 to x=1 cocksure integers elect to be n: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. The calculations to find the rations have been work show up using excel and the formula created using the fundamental theories of desegregation:...If you want to get a full essay, order it on our website: BestEssayCheap.com

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