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

paglia

sin^3x + cos^4x

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. LagrangeSon678
    Best Response
    You've already chosen the best response.
    Medals 0

    what is the problem here?

    • 2 years ago
  2. paglia
    Best Response
    You've already chosen the best response.
    Medals 1

    how to integrate, sorry!

    • 2 years ago
  3. LagrangeSon678
    Best Response
    You've already chosen the best response.
    Medals 0

    Well, if the power of sine is odd and positive , what you want to do is lop of one of the sine factor, put it to the right of the rest of the expression and convert the remaining (even) sine factors to cosines withe the Pythagorean identity , and then integrate with the substitution method where u=cos(x)

    • 2 years ago
  4. LagrangeSon678
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1325279411322:dw|

    • 2 years ago
  5. paglia
    Best Response
    You've already chosen the best response.
    Medals 1

    oh, ok, then, thanks.

    • 2 years ago
  6. LagrangeSon678
    Best Response
    You've already chosen the best response.
    Medals 0

    hold on let me finish it for you: \[\int sin^3(x)cos^4(x)dx =\int sin^2(x)cos^4(x)sin(x)dx\]

    • 2 years ago
  7. paglia
    Best Response
    You've already chosen the best response.
    Medals 1

    :D

    • 2 years ago
  8. LagrangeSon678
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int sin^2(x)cos^4(x)sin(x)dx=\int (1-cos^2(x))cos^4(x)sin(x)dx\]

    • 2 years ago
  9. LagrangeSon678
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int (1-cos^2(x))cos^4(x)sin(x)dx=\int (cos^4(x)-cos^6(x))sin(x)dx\]

    • 2 years ago
  10. LagrangeSon678
    Best Response
    You've already chosen the best response.
    Medals 0

    \[u=cos(x)\rightarrow \frac{du}{dx}=-sin(x)\rightarrow du=-sin(x)dx\rightarrow \frac{-du}{sin(x)}=dx\]

    • 2 years ago
  11. LagrangeSon678
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int (cos^4(x)-cos^6(x))sin(x)dx=-\int (u^4-u^6)du\]

    • 2 years ago
  12. LagrangeSon678
    Best Response
    You've already chosen the best response.
    Medals 0

    \[=-\int (u^4-u^6)du=-\frac{1}{5}u^5+\frac{1}{7}u^7+C\]

    • 2 years ago
  13. LagrangeSon678
    Best Response
    You've already chosen the best response.
    Medals 0

    \[=\frac{1}{7}cos^7(x)-\frac{1}{5}cos^5(x)+C\]

    • 2 years ago
  14. LagrangeSon678
    Best Response
    You've already chosen the best response.
    Medals 0

    And thats your answer

    • 2 years ago
  15. paglia
    Best Response
    You've already chosen the best response.
    Medals 1

    so simple. thanks!

    • 2 years ago
  16. LagrangeSon678
    Best Response
    You've already chosen the best response.
    Medals 0

    well, its simple once you see it

    • 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.