Turn on thread page Beta
    • Thread Starter
    Online

    12
    ReputationRep:
    ∫xsin0.5x dx with limits 0.5pi and zero

    u=x
    du/dx=1

    v=-0.5cos0.5x
    dv/dx=sin0.5x

    =uv-∫du/dxv
    =(x)(-1/2cos0.5x)-∫-0.5cos0.5x
    =(x)(-1/2cos0.5x)+0.25sin0.5x
    applying the limits to this ^ gives me:
    (-1/4pi(√2/2)+1/4(√2/2)+1/2

    However the answer in the text book states:
    0.5√2(4-π)??
    Offline

    21
    ReputationRep:
    (Original post by Chelsea12345)
    ∫xsin0.5x dx with limits 0.5pi and zero

    u=x
    du/dx=1

    v=-0.5cos0.5x
    dv/dx=sin0.5x

    =uv-∫du/dxv
    =(x)(-1/2cos0.5x)-∫-0.5cos0.5x
    =(x)(-1/2cos0.5x)+0.25sin0.5x
    applying the limits to this ^ gives me:
    (-1/4pi(√2/2)+1/4(√2/2)+1/2

    However the answer in the text book states:
    0.5√2(4-π)??
    you integrates sin(0.5x) wrong you should get -2cos(0.5x)
    • Community Assistant
    Offline

    17
    ReputationRep:
    Community Assistant
    The textbook is correct. You made a mistake integrating.

    u=x --> du=dx
    v = integral sin(0.5x) dx = -2cos(0.5x)

    So uv-integral v du is...?

    I think you're confusing derivative rules with integral ones.
    • Thread Starter
    Online

    12
    ReputationRep:
    using the right integral this time, i get :
    =-2xcos0.5x +4sin0.5x
    applying the limits to this^
    -√2/2pi +2√2 -1, is this just a simpified version of the textbook answer or have i made a mistake somewhere when applying the limits?
    • Community Assistant
    Offline

    17
    ReputationRep:
    Community Assistant
    (Original post by Chelsea12345)
    using the right integral this time, i get :
    =-2xcos0.5x +4sin0.5x
    applying the limits to this^
    -√2/2pi +2√2 -1, is this just a simpified version of the textbook answer or have i made a mistake somewhere when applying the limits?
    F(pi/2) - F(0) whereby F(x) is your integral simplifies to -2(pi/2)(root 2/2) + 4(root 2/2) = -pi root 2 / 2 + 2 root 2 = 2 root 2 - pi root 2 / 2 = root 2/2 [4-pi].
    • Thread Starter
    Online

    12
    ReputationRep:
    (Original post by thekidwhogames)
    F(pi/2) - F(0) whereby F(x) is your integral simplifies to -2(pi/2)(root 2/2) + 4(root 2/2) = -pi root 2 / 2 + 2 root 2 = 2 root 2 - pi root 2 / 2 = root 2/2 [4-pi].
    Thankyou!
    • Community Assistant
    Offline

    17
    ReputationRep:
    Community Assistant
    (Original post by Chelsea12345)
    Thankyou!
    No problem.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: February 3, 2018
The home of Results and Clearing

3,792

people online now

1,567,000

students helped last year

University open days

  1. Bournemouth University
    Clearing Open Day Undergraduate
    Fri, 17 Aug '18
  2. University of Bolton
    Undergraduate Open Day Undergraduate
    Fri, 17 Aug '18
  3. Bishop Grosseteste University
    All Courses Undergraduate
    Fri, 17 Aug '18
Poll
A-level students - how do you feel about your results?
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.