Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

agentx5

I need some help with checking this answer please: \[\large\int\limits_4^5 \frac{x^3-3 x^2-9}{x^3-3 x^2} dx = x-\frac{3}{x}-\ln|3-x|+\ln|x|+C\] I got this far using the partial fractions technique. I went to check my answer that I got on paper but Wolfram gives some craziness with hyperbolic tangents that I don't understand. So what should the answer be and wouldn't the natural log of 3-x be an issue because it gives non-real values? The correct answer MUST have real values and be in terms of constants and logs. If somebody could show me what's going on here it would be great :-)

  • one year ago
  • one year ago

  • This Question is Closed
  1. agentx5
    Best Response
    You've already chosen the best response.
    Medals 0

    For my partial fractions I got: \[x^3-3x^2-9=\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x-3}\] The A part turns into ln|x|, the B part turns into 3/x, the C part turns into -ln|3-x|

    • one year ago
  2. helder_edwin
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \Large \int\frac{x^3-3x^2-9}{x^3-3x^2}\,dx= \int\,dx-\int\frac{9}{x^2(x-3)}\,dx \] so you have to solve \[ \Large \frac{9}{x^2(x-3)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x-3} \]

    • one year ago
  3. Valpey
    Best Response
    You've already chosen the best response.
    Medals 0

    Well, for one thing you have written the natural log of the absolute value of 3-x.

    • one year ago
  4. agentx5
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah I used long division initially to pull out this: \[1 + \frac{-9}{x^3-3x^2}\]

    • one year ago
  5. agentx5
    Best Response
    You've already chosen the best response.
    Medals 0

    Integral of one with respect to x is just x, logically

    • one year ago
  6. agentx5
    Best Response
    You've already chosen the best response.
    Medals 0

    I think I mistyped my second post, sry @helder_edwin

    • one year ago
  7. agentx5
    Best Response
    You've already chosen the best response.
    Medals 0

    @Valpey oh yeah... so it's always a positive...

    • one year ago
  8. agentx5
    Best Response
    You've already chosen the best response.
    Medals 0

    ln|3-(4)| = ln|-1| = ln 1 = 0

    • one year ago
  9. agentx5
    Best Response
    You've already chosen the best response.
    Medals 0

    That's a nice simplification

    • one year ago
  10. agentx5
    Best Response
    You've already chosen the best response.
    Medals 0

    /me waves hello @asnaseer :-) ty for stopping by!

    • one year ago
  11. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 2

    you didn't need to do long division to simplify this in the first place. you could just have done this:\[\frac{x^3-3x^2-9}{x^3-3x^2}=\frac{x^3-3x^2}{x^3-3x^2}-\frac{9}{x^3-3x^2}=1-\frac{9}{x^3-3x^2}\]

    • one year ago
  12. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 2

    secondly, the logs should not contain the absolute value symbols around them

    • one year ago
  13. agentx5
    Best Response
    You've already chosen the best response.
    Medals 0

    Good point @asnaseer and why not? Without it wouldn't I have a non-real answer issue when I go to evaluate?

    • one year ago
  14. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 2

    you should have done this:\[\int\limits_4^5 \frac{x^3-3 x^2-9}{x^3-3 x^2} dx =[ x-\frac{3}{x}-\ln(3-x)+\ln(x)]_4^5\]\[\qquad=[x-\frac{3}{x}+ln(\frac{x}{3-x})]_4^5\]\[\qquad=(5-\frac{3}{5}+ln(-\frac{5}{2}))-(4-\frac{3}{4}+ln(-\frac{4}{1}))\]\[\qquad=5-\frac{3}{5}-4+\frac{3}{4}+ln(-\frac{5}{2}\div-\frac{4}{1})\]

    • one year ago
  15. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 2

    and the minuses cancel out inside the logs

    • one year ago
  16. agentx5
    Best Response
    You've already chosen the best response.
    Medals 0

    *reading carefully*

    • one year ago
  17. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 2

    BTW: waves hello back to @agentx5 :)

    • one year ago
  18. agentx5
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh... properties of logs... \[\ln|a|-\ln|b|=\ln|\frac{a}{b}|\]

    • one year ago
  19. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 2

    yes - but you shouldn't use the '|' symbols here

    • one year ago
  20. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 2

    as they usually indicate absolute value

    • one year ago
  21. agentx5
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\qquad=5-\frac{3}{5}-4+\frac{3}{4}+ln(-\frac{5}{2}\div-\frac{4}{1}) \approx 3.45258\] Disagrees with this check: http://www.wolframalpha.com/input/?i=integrate+from+4+to+5+for+%28x^3-3x^2-9%29%2F%28x^3-3x^2%29 \(\approx \frac{17}{25}\)

    • one year ago
  22. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 2

    I work it out to be exactly the same as the answer wolfram gives

    • one year ago
  23. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 2

    I get:\[\frac{23}{20}+ln(\frac{5}{8})\approx 0.68\]

    • one year ago
  24. agentx5
    Best Response
    You've already chosen the best response.
    Medals 0

    Ugh I see now I used the wrong base log on my calculator... /facepalm

    • one year ago
  25. agentx5
    Best Response
    You've already chosen the best response.
    Medals 0

    Derp.

    • one year ago
  26. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 2

    np :)

    • one year ago
  27. agentx5
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you so much you were a great help! @TuringTest give that claymation-man a medal ^_^

    • one year ago
  28. asnaseer
    Best Response
    You've already chosen the best response.
    Medals 2

    you are more than welcome my friend! :)

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.