Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    2
    ReputationRep:
    How to integrate sin(6x)cos(9x)??
    Offline

    2
    ReputationRep:
    (Original post by mil88)
    How to integrate sin(6x)cos(9x)??
    Have you covered complex integration yet?
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Calzs34)
    Have you covered integration by parts yet?
    Yes I have but firstly, I believe that by parts will not solve it as when you differentiate the trig function, you end up with another.
    Offline

    3
    ReputationRep:
    (Original post by mil88)
    How to integrate sin(6x)cos(9x)??
    Try using one of these product to sum formulae
    Attached Images
     
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by kingaaran)
    Try using one of these product to sum formulae
    Ok thanks, btw are they on the formula sheet (how did you find out about them?)
    Offline

    2
    ReputationRep:
    (Original post by mil88)
    Yes I have but firstly, I believe that by parts will not solve it as when you differentiate the trig function, you end up with another.
    Sorry, you're right - parts wouldn't work as you'll end up with a cycle of trig functions I edited it, you're supposed to use the equations as above stated by KingAaran.
    Offline

    3
    ReputationRep:
    (Original post by mil88)
    Ok thanks, btw are they on the formula sheet (how did you find out about them?)
    They are on the formula sheet It is usually quite helpful in such cases, because you can split the integral into one involving sin(ax) and one involving cos(bx) which makes it relatively simplistic after!
    Offline

    11
    ReputationRep:
    Parts would work:
    

\displaystyle

\begin{align*} I &= \int \sin6x\cos9xdx\\&= g(x) - a\int\cos6x\sin9xdx\\&= g(x) - a\left( h(x) - b\int \sin6x\cos9xdx\right )\\&= g(x) - a\left( h(x) - bI\right)\\\end{align*}
    Solve for I
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by kingaaran)
    They are on the formula sheet It is usually quite helpful in such cases, because you can split the integral into one involving sin(ax) and one involving cos(bx) which makes it relatively simplistic after!
    Indeed.
    Offline

    22
    ReputationRep:
    (Original post by MathsAndChess)
    Parts would work:
    ...
    But very overkill!
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by MathsAndChess)
    Parts would work:
    

\displaystyle<div style="text-align: center;">\begin{align*} I &= \int \sin6x\cos9xdx\\&= g(x) - a\int\cos6x\sin9xdx\\&= g(x) - a\left( h(x) - b\int \sin6x\cos9xdx\right )\\&= g(x) - a\left( h(x) - bI\right)\\\end{align*}</div>
    Ok thanks!
    Offline

    3
    ReputationRep:
    (Original post by Zacken)
    But very overkill!
    Indeeeeeed my man holding a trophy over his head
    Offline

    11
    ReputationRep:
    Overkill is the way to do it man..
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What's your favourite Christmas sweets?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.