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

    2
    ReputationRep:
    What is the integral of sin^2x times cos^2x dx.
    Offline

    14
    ReputationRep:
    (Original post by patterson)
    What is the integral of sin^2x times cos^2x dx.
    Remember sin2x = 2sinx cosx

    Now it should be simple.
    • Political Ambassador
    Offline

    3
    ReputationRep:
    Political Ambassador
    (Original post by patterson)
    What is the integral of sin^2x times cos^2x dx.
    \sin 2x = 2\sin x \cos x

    Then use an identity for sin squared.
    Offline

    1
    ReputationRep:
    Well, one way would be to use two trig identities, namely:

    sin2x=sinxcosx

    cos2x=1-2sin^2(x)
    Offline

    1
    ReputationRep:
    Alternatively, you can use the substitution u=1-sinx
    • Thread Starter
    Offline

    2
    ReputationRep:
    I was more looking for a method and answer
    Offline

    1
    ReputationRep:
    We basically spelled out the method to you. For an answer, just type it into http://wolframalpha.com .
    Offline

    11
    ReputationRep:
    (Original post by patterson)
    I was more looking for a method and answer
    What is \ (2 sin x cos x)^2
    • Study Helper
    Offline

    16
    ReputationRep:
    Study Helper
    (Original post by patterson)
    I was more looking for a method and answer
    the method is as follows:
    use a double angle formula to replace sinx cosx with an alternative form
    use another double angle formula to replace sin^2 (something) with a double-angle alternative
    integrate the result of the above 2 steps

    The answer will be what comes out.

    Post your working and then someone can check for you if you're unsure.
 
 
 
  • 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
    Brussels sprouts
    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.