Integrating Using Linear Partial Fractions
Hannah Hill
6 min read
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Study Guide Overview
This study guide covers linear partial fractions for integration in AP Calculus BC. It explains partial fraction decomposition, breaking down a rational function into simpler fractions for easier integration. The guide outlines the steps involved, including factoring the denominator, using undetermined coefficients, and solving for the coefficients. It provides examples demonstrating the process with factored and unfactored denominators and discusses when to apply this technique.
#6.12 Using Linear Partial Fractions
So you might be thinking that a BC-only technique for integration is extremely difficult, but worry no more, linear partial fractions are here to help you! Personally, this was my favorite integration technique throughout the unit and is the most time-saving.
#🤔 Understanding Partial Fraction Decomposition
In essence, partial fraction decomposition involves breaking down a fraction with a polynomial numerator and denominator into a sum of simpler fractions. This process relies on the fact that any rational function with a polynomial numerator and denominator can be expressed as a sum of partial fractions. The process transforms a complex fraction into a sum of simpler fractions, making it easier to integrate.
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Image representing a partial fraction decomposition
Image Courtesy of Cuemath
To begin, we first need to factor the denominator of the rational function into its distinct linear factors. If the denominator is not factorable, we can use long division to convert the rational function into a polynomial plus a remainder, in which the remainder is divided by a factorable denominator.
Next, we use the method of undetermined coefficients to find the coefficients of the partial fraction decomposition. This i...
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