Evaluate the integral. 0 to 1 (x3 - 5x - 11)/(x2 - x - 6) dx

Question

I tried it and got A= 1/5 and B=-7/5. Not sure about it. Thanks. 

Answer 1

Did you do long division first? Since this is of the form P(x)/Q(x) and P(x) is higher order than Q(x), the form is improper. You must perform long division first. Doing that you get (x+1) with remainder (2x+5)/(x²-x-6). Add those together gives

 

(x³-5x-11)/(x²-x-6) = (x+1) + (2x+5)/(x²-x-6)

 

Now you can factor the denominator in the second term and perform a partial fraction decomposition. I have (x-3) as my A-term and (x+2) as my B-term. Then I get A = 11/5 and B = -1/5. Here is my expansion.

 

(x³-5x-11)/(x²-x-6) = (x+1) + (11/5)(1/(x-3)) - (1/5)(1/(x+2))

 

I hope this helps you out.

Answer 2

You have to first multiply the two trinomials.  Then integrate by taking the anti-derivative of each term and then evaluate by substituting.  It is easy to make an arithmetic error.  If I did not make an arithmetic error the answer is 4703/60.  I don't know what you think A and B is.  If you call me I'll be glad to explain how the problem is done.  There no obligation if you call me.  Mike C. 732-547-8661