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teng125
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how to integ 2x^2 / (1-x^2)
using partial fracton??
using partial fracton??
Partial fraction decomposition is a method used to break down a complex fraction into simpler fractions. This is done by expressing the complex fraction as a sum of simpler fractions with unique denominators.
Partial fraction decomposition is used to simplify integration problems, especially when dealing with rational functions. It allows us to integrate each simpler fraction separately, making the overall integration process easier.
To determine the partial fraction decomposition of a fraction, you need to follow a specific set of steps. First, factor the denominator of the fraction into irreducible factors. Then, set up a system of equations using the coefficients of each term in the numerator and solve for the unknown variables. Finally, substitute the values of the variables into the partial fraction decomposition form and combine like terms.
Yes, for example, if we want to integrate 2x^2 / (1-x^2) using partial fraction decomposition, we would first factor the denominator to get (1-x)(1+x). Then, we would set up the equation 2x^2 / (1-x)(1+x) = A/(1-x) + B/(1+x) and solve for A and B. Once we have the values of A and B, we can substitute them into the partial fraction decomposition form and integrate each simpler fraction separately.
Yes, there are a few restrictions to keep in mind when using partial fraction decomposition. First, the denominator of the original fraction must be factorable into linear and irreducible quadratic terms. Second, each irreducible quadratic factor must have a unique coefficient. Lastly, the degree of the numerator must be less than the degree of the denominator.