If the following function can be expressed in partial fractions as shown: y = \dfrac{1}{(x + 1)(x...
Question:
If the following function can be expressed in partial fractions as shown:
{eq}y = \dfrac{1}{(x + 1)(x - 2)} = \dfrac{A}{(x + 1)} + \dfrac{B}{(x - 2)} {/eq}
find the values of {eq}A {/eq} and {eq}B {/eq}. Hence integrate this function.
Partial Fraction Form of a Function:
The partial fraction form of rational function {eq}\frac{{px + q}}{{\left( {x - a} \right)\left( {x - b} \right)}} {/eq} is given as {eq}\frac{A}{{\left( {x - a} \right)}} + \frac{B}{{\left( {x - b} \right)}} {/eq}. Multiply the equation by the denominators and then compare the coefficients to obtain the values of {eq}A {/eq} and {eq}B {/eq}. Hereafter, integrate the equation using basic integration rules.
Answer and Explanation: 1
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- The function is {eq}y = \frac{1}{{\left( {x + 1} \right)\left( {x - 2} \right)}} {/eq} and it is expressed in partial fraction as...
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Chapter 3 / Lesson 25Learn about how to carry out partial fraction decomposition with polynomial fractions. Discover example equations and walkthroughs of partial fraction decomposition.