The discussion revolves around evaluating the integral of a rational function involving polynomial long division. The specific integral is \(\int^1_0 \frac{-3x^3+12x+30}{x^2-x-6}dx\), where participants are exploring the long division of the numerator by the denominator.
Some participants have provided clarifications regarding the long division process, indicating that it should conclude when the degree of the remainder is less than that of the divisor. There is an acknowledgment of differing interpretations about the division's outcome, but no consensus has been reached.
There is a focus on the polynomial's factors and the conditions under which long division is considered complete. Participants are navigating the implications of their findings without definitive conclusions.
The division ends when the degree of the remainder is less than the degree of the divisor. In this case, when the remainder is of the form Cx+D, you're done. The result of your division will be thattheRukus said:Homework Statement
\int^1_0 \frac{-3x^3+12x+30}{x^2-x-6}dxHomework Equations
The Attempt at a Solution
I've attempted long division, but the long division does not seem to come to an end.. I'm not sure what to make of this.. If the long division does not end, does this mean that the polynomial has no factors...? I'm confused, can someone give me a push in the right direction?
Thanks PhysicsForums!
The long division does come to an end. You should have gotten -3x - 3 + <remainder>/(x2 - x - 6).theRukus said:Homework Statement
\int^1_0 \frac{-3x^3+12x+30}{x^2-x-6}dx
Homework Equations
The Attempt at a Solution
I've attempted long division, but the long division does not seem to come to an end.. I'm not sure what to make of this.. If the long division does not end, does this mean that the polynomial has no factors...? I'm confused, can someone give me a push in the right direction?
Thanks PhysicsForums!