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

    0
    ReputationRep:
    ( 1 + sin x ) ^2 dx
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by IShouldBeRevising_)
    ( 1 + sin x ) ^2 dx
    Expand and integrate term by term.

    For \sin^2 x use the sine double angle formula.
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    Expand the bracket.

    There is a standard method you should use to integrate \sin^2 x with respect to x. Trawl back through your notes. It is very important and involves a trigonometric identity.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Mr M)
    Expand the bracket.

    There is a standard method you should use to integrate \sin^2 x with respect to x. Trawl back through your notes. It is very important and involves a trigonometric identity.
    Do you get

    X - 2COSX + 1/4(2x - sin2x)
    Offline

    11
    ReputationRep:
    (Original post by IShouldBeRevising_)
    Do you get

    X - 2COSX + 1/4(2x - sin2x)
    Not quite there's a constant of integration missing, and its good practice to collect like terms.
    Also
    Spoiler:
    Show
    cos(x) => +sin(x)
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by joostan)
    Not quite there's a constant of integration missing, and its good practice to collect like terms.
    Also
    Spoiler:
    Show
    cos(x) => +sin(x)
    What about

    x - 2cosx + 1/4(2x - sin2x) + c
    Offline

    11
    ReputationRep:
    (Original post by IShouldBeRevising_)
    What about

    x - 2cosx + 1/4(2x - sin2x) + c
    Correct, though like I said, collecting like terms is good practice.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by joostan)
    Correct, though like I said, collecting like terms is good practice.
    What would the answer be if you collected like terms?
    Offline

    11
    ReputationRep:
    (Original post by IShouldBeRevising_)
    What would the answer be if you collected like terms?
    3/2x - 2cos(x) - sin(2x)/4 +c
    Or if you like:
    1/4(6x - 8cos(x) - sin(2x)) +c
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by joostan)
    3/2x - 2cos(x) - sin(2x)/4 +c
    Or if you like:
    1/4(6x - 8cos(x) - sin(2x)) +c
    Ok thanks for your help I cant seem to get the correct answer the question has the limits pi/4 and 0

    I have subbed these in to the answer and im getting completely the wrong answer
    Offline

    11
    ReputationRep:
    (Original post by IShouldBeRevising_)
    Ok thanks for your help I cant seem to get the correct answer the question has the limits pi/4 and 0

    I have subbed these in to the answer and im getting completely the wrong answer
    What did you get?
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by joostan)
    What did you get?
    A decimal
    Offline

    11
    ReputationRep:
    (Original post by IShouldBeRevising_)
    A decimal
    1.513883683?
    This is integral can be evaluated exactly. . .
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by joostan)
    1.513883683?
    This is integral can be evaluated exactly. . .
    Yeah thanks the answer is in exact form.
    Offline

    11
    ReputationRep:
    (Original post by IShouldBeRevising_)
    Yeah thanks the answer is in exact form.
    Do you know the values for cos(0), sin(0), cos(pi/4) and sin(pi/2)?
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
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.