Turn on thread page Beta
    • Thread Starter
    Offline

    1
    ReputationRep:
    how would integrate this ...

    ∫ 2 sin 3x sin 2x dx.
    Offline

    15
    (Original post by Raysfc16)
    how would integrate this ...

    ∫ 2 sin 3x sin 2x dx.
    Use trigonometry to change the form of the integrand.
    Spoiler:
    Show
    Hint:
    Expand \cos(A-B)-\cos(A+B)
    Offline

    22
    ReputationRep:
    (Original post by Raysfc16)
    how would integrate this ...

    ∫ 2 sin 3x sin 2x dx.
    Use your formula booklet. Under the C3 section, it clearly states that -2 \sin \frac{A+B}{2} \sin \frac{A-B}{2} = \cos A - \cos B.

    Use this in the case that A+B = 6x and A-B= 4x, so A=5x and B = x.

    This gives you \displaystyle -\int -2\sin 3x \sin 2x \, \mathrm{d}x = -\int \cos 5x - \cos x \, \mathrm{d}x = \int \cos x - \cos 5x \, \mathrm{d}x
    Offline

    22
    ReputationRep:
    Oh, and moved to maths.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by EricPiphany)
    Use trigonometry to change the form of the integrand.
    Spoiler:
    Show
    Hint:
    Expand \cos(A-B)-\cos(A+B)
    (Original post by Zacken)
    Use your formula booklet. Under the C3 section, it clearly states that -2 \sin \frac{A+B}{2} \sin \frac{A-B}{2} = \cos A - \cos B.

    Use this in the case that A+B = 6x and A-B= 4x, so A=5x and B = x.

    This gives you \displaystyle -\int -2\sin 3x \sin 2x \, \mathrm{d}x = -\int \cos 5x - \cos x \, \mathrm{d}x = \int \cos x - \cos 5x \, \mathrm{d}x



    thank you so much guys!
    Offline

    22
    ReputationRep:
    (Original post by Raysfc16)
    thank you so much guys!
    Pleasure.
    Offline

    19
    ReputationRep:
    It can also be done by parts
    Offline

    15
    (Original post by TeeEm)
    It can also be done by parts
    Twice? I'm going to try it
    Offline

    19
    ReputationRep:
    (Original post by EricPiphany)
    Twice? I'm going to try it
    Indeed
    Just as quick but not widely known
    Offline

    22
    ReputationRep:
    (Original post by EricPiphany)
    Twice? I'm going to try it
    Cyclic IBP's, the kind where you need to re-arrange and solve for I. It's not as quick as spotting the trig simplification, though.
    Offline

    15
    (Original post by TeeEm)
    Indeed
    Just as quick but not widely known
    Just as quick?
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: March 9, 2016

University open days

  1. University of Bradford
    University-wide Postgraduate
    Wed, 25 Jul '18
  2. University of Buckingham
    Psychology Taster Tutorial Undergraduate
    Wed, 25 Jul '18
  3. Bournemouth University
    Clearing Campus Visit Undergraduate
    Wed, 1 Aug '18
Poll
How are you feeling in the run-up to Results Day 2018?
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

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

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