How do you integrate #(x^3-4x-10)/(x^2-x-6)# using partial fractions?
1 Answer
- Ski-Doo is the number one brand of snowmobiles in the world, with models from high performance to utility, and with clean 2-stroke and 4-stroke engines.
- Its too simple If f(x) is continuos and takes up only rational values then f(x) has to be a constant function.If not so,then it will take irrational values too. So f(x) is constant function and f(2) is 10 so f(1.5) will also be equal to f(2) and w.
Explanation:
The first step is to factor the denominator of the function
Example: Solve x 3 + 6x 2 + 9x + 6 = 0. A = 6, b = 9, c = 6. Then d = 3z + 6, e = 3z 2 + 12z + 9, f = z 3 + 6z 2 + 9z + 6. Then g = a 2 - 3b = 36 - 27 = 9, h = ab - 9c = 54 - 54 = 0, i = b 2 - 3ac = 81 - 108 = -27. In fact, if you took 1/3 of one pizza, filled in the missing part of the other, you would be left with one full pizza, and 1/3 of another (because you took 1/3 away from 2/3). Now in math language: When adding fractions with a common denominator, you just add the numerators and keep the same denominator. Thus, 2/3+ 2/3 = 4/3.
since the factors are linear then the coefficients of the partial fractions will be constants , say A and B. Writing the function in terms of it's partial fractions.
multiplying through by (x-3)(x+2)
We now have to find the values of A and B .Note that if x = -2 the term with A will be zero and if x = 3 the term with B will be zero. We can make use of this fact in finding A and B. Ytd video downloader pro 4 4 0 x.
let x = -2 in (1) :- 10 = -5B #rArrcolor(blue)' B = 2'#
Hot door cadtools 12 1 1 cr2 download free. let x = 3 in (1) : 5 = 5A #rArr color(blue)' A = 1 '#
Integral becomes : #int(dx)/(x-3) + int(2dx)/(x+2) #
Related topic
![Doo 2 3 3 X 2 Doo 2 3 3 X 2](https://tel.img.pmdstatic.net/fit/https.3A.2F.2Fprd2-tel-epg-img.2Es3-eu-west-1.2Eamazonaws.2Ecom.2Fprogram.2F585fc0297cb095f4.2Ejpg/1200x630/crop-from/top/quality/80/cr/wqkgV2FybmVyIEJyb3MgRW50ZXJ0YWluZW1lbnQgSW5jLg%3D%3D/scooby-doo-2-les-monstres-se-dechainent.jpg)