coookiemonste said:The Attempt at a Solution
1=A/(x+a) + B/(x+b)
1=B(x+a) + A(x+b)
1=Bx+ Ba + Ax +Ab
so 0=Bx+ Ax, 1=Ba+Ab
A=-B, 1=B(a-b)
∫-1/(x+a) +∫1/(x+b)
Im not sure if I am headed in the right direction or not.
The equation 1= B(a-b) settles that.muso07 said:How do you know what A and B equal? You don't know numerical values, just what they're equal to in relation to one another.
gabbagabbahey is right, you should get B∫-1/(x+a) +B∫1/(x+b)
Now what do you know about the integral of 1/x ?
Partial fractions are a method used in calculus to simplify and evaluate complex rational expressions. They are used to break down a single fraction into smaller, more manageable fractions that are easier to integrate or manipulate.
To solve a partial fractions problem, you first need to factor the denominator into linear or quadratic factors. Then, you set up a system of equations using the unknown coefficients for each factor. Finally, you solve for the coefficients and rewrite the original expression as a sum of the partial fractions.
A proper partial fraction has a denominator with a higher degree than the numerator, meaning the fraction is less than one. An improper partial fraction has a numerator with a higher degree than the denominator, making the fraction greater than one.
Yes, partial fractions can be used to integrate rational functions. By breaking down a complex rational function into smaller fractions, integration becomes easier and more manageable. This method is commonly used in calculus to solve integrals involving rational functions.
Yes, there are some limitations and restrictions when using partial fractions. The denominator of the original fraction must be factorable into linear or quadratic factors. Additionally, the factors must be distinct and irreducible, meaning they cannot be further simplified. If these conditions are not met, the partial fractions method may not be applicable.