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

Kelumptus Group Title

Solution to the following integral (in post below)

  • 2 years ago
  • 2 years ago

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

    \[\int\limits_{}^{} \frac{t-1}{t^{2}+4t+3} dt\] I'm kind of stuck on this one, i've tried a few different methods of u substitution but can't solve it.

    • 2 years ago
  2. Callisto Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    Does partial fraction help?

    • 2 years ago
  3. Kelumptus Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah i think that might be the answer. I have only done partial fractions in the form where there is a coefficient and a variable however. Not when there are two terms in the numerator.

    • 2 years ago
  4. Callisto Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    Hmmm... \[\frac{t-1}{t^{2}+4t+3}=\frac{t-1}{(t+1)(t+3)} = \frac{A}{t+1}+\frac{B}{t+3}\] So, A(t+3) + B(t+1) = t-1 Comparing the coefficients, A+B = 1 3A +B = -1 Something like this?!

    • 2 years ago
  5. Kelumptus Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Yep... i think i jumped the gun when i gave up on trying to solve with partial fractions. I just revised my notes and i'll have a go using partial fractions now. I'll let you know how i go.

    • 2 years ago
  6. Callisto Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    Okay!!~

    • 2 years ago
  7. Kelumptus Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Awesome, partial fractions was the key. Thanks for that =)

    • 2 years ago
  8. Callisto Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    You're welcome :)

    • 2 years ago
  9. sehanhasan Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Use partial fraction method..

    • 2 years ago
  10. shubhamsrg Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    or you may use partial fractions alternatively, what i mean is t-1 / t^2 +4t +3 = 1/2 ( 2t - 2)/(t^2 +4t +3) =1/2 ( 2t +4 -6)/(t^2 +4t +3) = 1/2 ( 2t +4)/(t^2 +4t +3) - 1/2 (6/(t^2 +4t +3)) integrate separately, for 1st part, if you let denominator =z,. you directly get numerator = dz .. we are concerned with integrating 1/(t^2 +4t +3) that's also simple, we see we have 1/(t+1)(t+3) = 1/2 (2 / (t+1)(t+3)) =1/2 ( t+3 - (t+1))/(t+1)(t+3)) =>now when you separate out, you'll directly be able to integrate ..hope that helps.. note that i've used partial fractions only,but in a different manner..

    • 2 years 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.