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

    0
    ReputationRep:
    Integrate cosx- sinx / 1+sin2x pls?
    Offline

    10
    ReputationRep:
    (Original post by Leon7308)
    Integrate cosx- sinx / 1+sin2x pls?
    I assume what you're trying to integrate here is (cos x - sin x)/ (1 + sin 2x).

    Two main trig formulas are needed here:
    cos^2(x)+sin^2(x) = 1 and
    sin (2x) = 2 cos (x) sin (x)

    Once you do these two subs, you'll have a fraction in a format where the lower bit of the fraction has something squared (X^2), and the upper bit has the differentiation of that something (X). Meaning that with some modifications, you can have the integral of ln (X) there!

    Multiply and divide by what's needed, and a few cancellations of terms will come along to leave you with one term to integrate!

    Let me know if you need more hints.
    • Official TSR Representative
    Offline

    11
    ReputationRep:
    (Original post by candyaljamila)
    I assume what you're trying to integrate here is (cos x - sin x)/ (1 + sin 2x).

    Two main trig formulas are needed here:
    cos^2(x)+sin^2(x) = 1 and
    sin (2x) = 2 cos (x) sin (x)

    Once you do these two subs, you'll have a fraction in a format where the lower bit of the fraction has something squared (X^2), and the upper bit has the differentiation of that something (X). Meaning that with some modifications, you can have the integral of ln (X) there!

    Multiply and divide by what's needed, and a few cancellations of terms will come along to leave you with one term to integrate!

    Let me know if you need more hints.

    In other words, the denominator will be of the form (a + b)^(2) = a^(2) + 2ab + b^(2).

    Once the numerator and denominator are sorted out you can use a substitution of the form u = ax + bx which leads to a nice solvable integral.

    This trick crops up quite often in Trig differentiation and integration. Another example is tan(x) + 2lnsec(x).
    Differentiating leads to sec^2(x) + 2tan(x). Using tan^2(x) + 1 = sec^2(x), you have tan^2(x) + 2tan(x) + 1. This
    is again a disguised form of a^(2) + 2ab + b^(2) = (a + b)^(2). So you can write it as (tan(x) + 1)^(2).

    If you get stuck on an integration or proof that 'looks impossible', it may help to remember the trick!
 
 
 
  • 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
    Did TEF Bronze Award affect your UCAS choices?
    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.