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

jotopia34 Group Title

What is the integral of 2sinx/1+cos^2x? I can't seem to get it :(

  • one year ago
  • one year ago

  • This Question is Closed
  1. jotopia34 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int\limits_{0}^{\pi/6}2sinx/1+\cos^2x\]

    • one year ago
  2. jotopia34 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I used u=cosx, but i got a weird quotient

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

    when u=cos x du =-sin x dx so, your new integral will be \(\int \dfrac{-2}{1+u^2}du\) did you got this ?

    • one year ago
  4. jotopia34 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes harnn i did but now can i just pull out the -2?

    • one year ago
  5. jotopia34 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh pellet, i think i see it, the bottom part is inverse tan right?

    • one year ago
  6. CanadianAsian Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    This is u substitution. Say that \[u = \cos x\] Then the derivative of u is: \[du = -sinxdx\] Then change your bounds: \[\cos(0) = 1\] which is your lower bound and your upper bound is: \[\cos(\Pi/6) = \frac{ \sqrt3 }{ 2 }\] So then you can substitute these into the equation to get \[\int\limits_{1}^{\frac{\sqrt3}{2}}\frac{ -2 }{ 1+u^2 }\] which is the same as \[-2\int\limits_{1}^{\frac{\sqrt3}{2}}\frac{ 1 }{ 1+u^2 }\] and \[\int\limits_{}^{}\frac{ 1 }{ 1 + u^2 }\] is just arctan. So just take \[-2*(\arctan(\frac{ \sqrt3 }{ 2 }) - \arctan(1))\] To get your answer.

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

    yes.

    • one year ago
  8. jotopia34 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thank u very much!!

    • 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.