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Ab L.

asked • 09/16/16

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

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

2 Answers By Expert Tutors

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Michael C. answered • 09/17/16

Tutor
5 (8)

Michael C. Mathematics Tutor

Michael W.

Hmmm, maybe the student did something with partial fractions to get an "A" and a "B," and is asking if those were right?  But Michael J is right:  it's a quotient, not a product.
 
Ab, if you're asking about partial fractions, and if I did the algebra correctly, I didn't quite get what you got.  I divided the top polynomial minus the bottom polynomial and got this:
 
x + 1 + (2x-5)/(x^2 - x - 6)
 
Hopefully, I didn't botch the long division!  I thiiiink it works.  That second piece needs to be integrated by partial fractions.  The denominator factors, and then you split up the fraction into two pieces:
 
A / (x-3) + B / (x + 2)
 
Is that the "A" and the "B" you're talking about?  If so, and if I did the math right, then my A and B don't quiiiite match yours.
 
Let me know if I'm following you, and then we can figure it out from there.
 
 
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09/17/16

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