Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

paglia

  • 4 years ago

sin^3x + cos^4x

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

    what is the problem here?

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

    how to integrate, sorry!

  3. LagrangeSon678
    • 4 years ago
    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)

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

    |dw:1325279411322:dw|

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

    oh, ok, then, thanks.

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

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

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

    :D

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

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

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

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

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

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

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

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

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

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

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

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

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

    And thats your answer

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

    so simple. thanks!

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

    well, its simple once you see it

  17. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy