Math Ia Investigating Ratios of Areas and Volumes

Math HL Internal Assessment INVESTIGATING RATIOS OF AREAS AND VOLUMES The office of this internal opinion is to investigate the ratios amongst the bea formed supra and beneath a work of the type y=xn utilize integrals. Integrals argon an essential part of calculus which suspends us to descend 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 to a lower place: This study allow for focus on leting a conjecture surrounded by 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 exit analyze several examples to extract a pattern and move up a conjecture, which will subsequent 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 heavens B, and the region betw een 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 upstanding 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 alliance between the ratios obtained and the initial function. In these setoff examples, n will only include positive integers, n ? ?+ Example calculations: 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 chosen 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 start using excel and the formula created using the fundamental theories of integration:...If you want to get a full essay, order it on our website: BestEssayCheap.com

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