All Flashcards
What is Partial Fraction Decomposition?
Breaking down a rational function into simpler fractions for easier integration.
Define 'Undetermined Coefficients' in PFD.
A method to find the coefficients of the partial fractions by solving a system of equations.
What is a rational function?
A function that can be expressed as a ratio of two polynomials.
What are linear factors in the context of PFD?
Factors in the denominator of the form (ax + b), where a and b are constants.
What is the general form for decomposing ?
What is the integral of ?
General form of PFD with three linear factors?
Explain the goal of Partial Fraction Decomposition.
To transform a complex rational function into a sum of simpler fractions that are easier to integrate.
Why is factoring the denominator important in PFD?
Factoring allows us to identify the individual fractions needed for the decomposition.
When should you consider using Partial Fraction Decomposition?
When integrating rational functions where the denominator can be factored into linear, non-repeating factors.
What is the relationship between the degree of the numerator and denominator for PFD?
The degree of the numerator should be less than the degree of the denominator. If not, use long division first.
Explain the purpose of solving for A, B, C, etc. in PFD.
These variables represent the numerators of the decomposed fractions, and finding their values allows us to rewrite the original integral.
What is the role of the '+C' in indefinite integrals?
It represents the constant of integration, accounting for all possible antiderivatives of a function.