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

sha0403 Group Title

help me to integrate this : integration of (3 sin^2 x cos x) dx i confuse how to integrate this..

  • one year ago
  • one year ago

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

    let sinx = t

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

    Use "u"-substitution since you see a function and its derivative next to it.

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

    • one year ago
    1 Attachment
  4. Kainui Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    www.wolframalpha.com show me steps

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

    ^^shown

    • one year ago
  6. Australopithecus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    you have to use identities to solve this \[\int\limits_{}^{}3 \sin^2 x \cos x\]

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

    ...

    • one year ago
  8. Australopithecus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[3\int\limits_{}^{}\sin^2 x \cos xdx\] \[3\int\limits_{}^{}(1-\cos^{2}(x)) \cos xdx\]

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

    No, sin^2(x)=u 1/2 du=cosxdx 3/2udu becomes your new integral.

    • one year ago
  10. Australopithecus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    f(x) = sin^2(x) f'(x) = cos(x)^2*sin(x)

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

    Why not u = sinx --> du = cosxdx ??

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

    = 3 ∫ u² du = ....

    • one year ago
  13. Australopithecus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[3(\int\limits_{}^{}\cos(x)dx - \int\limits_{}^{}\cos^2(x)dx)\]

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

    It's crystal clear about the relation between sinx and cosxdx :)

    • one year ago
  15. Australopithecus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    remember for the future \[\cos^2(x) = \frac{1 + \cos(2x)}{2}\] so we have, \[3(\sin(x) + c - \int\limits_{}^{}\frac{1+\cos(2x)}{2}dx)\]

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

    ^done in 3rd reply

    • one year ago
  17. Australopithecus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    You can solve it my way too which is good practice for when you get integrals with trig functions to high powers

    • one year ago
  18. shubhamsrg Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @Australopithecus its cos^3 x there and not square

    • one year ago
  19. Australopithecus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    oh sorry made a mistake lol

    • one year ago
  20. sha0403 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    where the best solution? i still confuse.. hu2

    • one year ago
  21. Australopithecus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    it can still be solved with that method

    • one year ago
  22. shubhamsrg Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    and sinx= t ,u whatever, thats the easiest thing which you can do..as i pointed out in the very beginning ..

    • one year ago
  23. shubhamsrg Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    cos^3 x will still involve substitution ..

    • one year ago
  24. Australopithecus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[3(\sin(x) + c - \int\limits_{}^{}\cos(x)\frac{1 + \cos(2x)}{2}dx\]

    • one year ago
  25. Australopithecus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm not arguing that substitution will be involved in my solution but it still works for solving this integral it is just the long way

    • one year ago
  26. Australopithecus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I think I made a mistake again though meh

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

    @Australopithecus It's like suggesting someone make a tunnel through a mountain when you can just use a teleporter.

    • one year ago
  28. Australopithecus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    It is still applicable and stop hassling me I'm rusty ha

    • one year ago
  29. sha0403 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so, the best solution? anyone?

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

    3rd

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

    @sha0403, to clarify, you should use any method provided except @Australopithecus'

    • one year ago
  32. sha0403 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok thanks u all for helping me..i appreciate it.. =)

    • 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.