Turn on thread page Beta

Can somebody clear up some trig differentiation/integration watch

    • Thread Starter
    Offline

    0
    ReputationRep:
    I am a little confused with:

    d/dx sin2x

    d/dx cos2x

    d/dx sin3x

    d/dx sin^2(x)

    d/dx cos^2(x)

    and the respective integrals, could somebody be kond enough to clear this up for me, many thanks in advance.
    Offline

    10
    ReputationRep:
    (Original post by rayman198)
    I am a little confused with:

    d/dx sin2x

    d/dx cos2x

    d/dx sin3x

    d/dx sin^2(x)

    d/dx cos^2(x)

    and the respective integrals, could somebody be kond enough to clear this up for me, many thanks in advance.
    The first 3 can be done by the chain rule.

    Let u=2x
    d/dx(sin2x) = d/du(sinu).du/dx
    = 2cosu
    = 2cos2x

    and the same goes for the other two; -2sin2x and 3cos3x

    to integrate them, you need to divide by the constant multiplying x rather than multiply by it.

    eg. INT sin2x dx = -0.5 cos 2x

    which you can verify by differentiation.

    cos^2(x) and sin^2(x) can be differentiated using the chain rule.
    let u = sinx
    d/dx(u^2) = 2u du/dx
    = 2sinx cosx

    To integrate them, use the double angle formula cos2x = 1-2sin^2(x) = 2cos^2(x) - 1
    and re-arrange to get cos^2(x) = 0.5 (1+cos2x) and sin^2(x) = 0.5 (1-sin2x)

    and you integrate as above.
    • Thread Starter
    Offline

    0
    ReputationRep:
    thanks for tha, you should be a teacher (if you arent already) il owe that extra 10% in my exam tomorrow to you!
    Offline

    14
    Generally  \frac{d}{dx} sin(f(x)) = f'(x)cos(f(x))
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: June 11, 2006

University open days

  • Manchester Metropolitan University
    Postgraduate Open Day Postgraduate
    Wed, 14 Nov '18
  • University of Chester
    Chester campuses Undergraduate
    Wed, 14 Nov '18
  • Anglia Ruskin University
    Ambitious, driven, developing your career & employability? Aspiring in your field, up-skilling after a career break? Then our Postgrad Open Evening is for you. Postgraduate
    Wed, 14 Nov '18
Poll
Have you ever experienced bullying?
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

Equations

Best calculators for A level Maths

Tips on which model to get

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.