Turn on thread page Beta

P3 integration help elpaw! watch

    • Thread Starter
    Offline

    13
    ReputationRep:
    I am stuck on 4 sticky questions:

    1)

    ∫(1/√(9- x^2)) dx

    Where definite limits are 0 -> 3

    2)

    ∫(1/(9 x^2 +4) dx

    Where limits are -∞ -> ∞

    3)

    ∫(1/[√(x(1-x))]) dx

    Where limits are 0 -> 1

    4)

    ∫(1/[(1+ x^2)^(3/2)]) dx

    As limits 1 -> →∞

    I am very much stuck on these trigonometric subsitutition integrations.
    Offline

    0
    ReputationRep:
    here's 1,The rest use a similar approach.
    Attached Images
     
    Offline

    15
    ReputationRep:
    Is this for edexcel?
    Offline

    1
    ReputationRep:
    (Original post by IntegralAnomaly)
    here's 1,The rest use a similar approach.
    How do we know that X=Sint, the poster hasn't specified the substitution.
    Offline

    8
    ReputationRep:
    (Original post by Hexa)
    I am stuck on 4 sticky questions:

    1)

    ∫(1/√(9- x^2)) dx

    Where definite limits are 0 -> 3
    I=∫(1/√(9- x^2)) dx
    I=(1/3)∫(1/√(1- (x/3)^2)) dx

    let x=3sinu
    dx=3cosudu

    I=(1/3)∫1/√(1-cos²u).3cosudu
    I=∫(1/cosu).cosudu
    I=∫1 du
    I=u
    I=arcsin(x/3){0,3}
    I=(arcsin(1) - arcsin(0))
    I=π/2 - 0
    I=π/2
    ====
    Offline

    10
    ReputationRep:
    (Original post by Bhaal85)
    How do we know that X=Sint, the poster hasn't specified the substitution.
    It's a standard thing, you use x = sin t so that the root gives you cos t. Though I'm not sure for P3 if you're meant to do it like that.
    • Thread Starter
    Offline

    13
    ReputationRep:
    So for 2) Shall I let (9/4)sin u = x?

    EDIT: I mean (2/3)sin u =x
    Offline

    0
    ReputationRep:
    2 looked juicy,so here:
    Attached Images
     
    Offline

    2
    ReputationRep:
    (Original post by imasillynarb)
    Is this for edexcel?
    Integration by substitution is in Edexcel P3, but I've always seen them give you the substitution.
    Offline

    2
    ReputationRep:
    The first two are standard results that are in the edexcel formula book, for three, complete the square on the denominator as 1/4 - (x - 1)² and use a standard result (or sub (x - 1) = 1/2 siny) etc
    Offline

    0
    ReputationRep:
    here's 3:
    Attached Images
     
    Offline

    2
    ReputationRep:
    For 4 use x = tanu
    Offline

    0
    ReputationRep:
    (Original post by Hexa)
    I am stuck on 4 sticky questions:

    1)

    ∫(1/√(9- x^2)) dx

    Where definite limits are 0 -> 3

    2)

    ∫(1/(9 x^2 +4) dx

    Where limits are -∞ -> ∞

    3)

    ∫(1/[√(x(1-x))]) dx

    Where limits are 0 -> 1

    4)

    ∫(1/[(1+ x^2)^(3/2)]) dx

    As limits 1 -> →∞

    I am very much stuck on these trigonometric subsitutition integrations.
    Try and have a go at 4,use the same procedure as for the rest,but think on an identity that will simplify (1+x^2)^(1/2).
    Offline

    15
    ReputationRep:
    (Original post by mockel)
    Integration by substitution is in Edexcel P3, but I've always seen them give you the substitution.
    Yeh integration by substitutions, but Ive never seen any questions like this: ie where you have to use/make your own trig substitutions
    • Thread Starter
    Offline

    13
    ReputationRep:
    Thank you so much people. I'm doing OCR btw, and the formulae book does not have the standard results.
    Offline

    0
    ReputationRep:
    these type of questions on edexcel will most prob be p5.If it comes up on p3,then they will tell u the relevent substitution.
    • Thread Starter
    Offline

    13
    ReputationRep:
    Unlucky me then, I'm on the rather tougher regieme.

    What subsitiution for this integral? (no need for answers, hints only)

    ∫(1/(x √(x^2 -1)) dx

    as definite limits: 1 -> ∞
    Offline

    0
    ReputationRep:
    (Original post by Hexa)
    Unlucky me then, I'm on the rather tougher regieme.

    What subsitiution for this integral? (no need for answers, hints only)

    ∫(1/(x √(x^2 -1)) dx

    as definite limits: 1 -> ∞
    think of the hyperbolic functions....................... ........
    Offline

    15
    ReputationRep:
    if they're not substitutions, they're standard inverse trigs/hyperbs, which are in the formula book (in edexcel anyway)
    Offline

    10
    ReputationRep:
    (Original post by IntegralAnomaly)
    think of the hyperbolic functions....................... ........
    They might not have covered them in P3 though.
 
 
 

University open days

  • Staffordshire University
    Everything except: Midwifery, Operating Department Practice, Paramedic Undergraduate
    Sun, 21 Oct '18
  • University of Exeter
    Undergraduate Open Days - Exeter Campus Undergraduate
    Wed, 24 Oct '18
  • University of Bradford
    Faculty of Health Studies Postgraduate
    Wed, 24 Oct '18
Poll
Who is most responsible for your success at university

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.