Hey there! Sign in to join this conversationNew here? Join for free

Integration help! Watch

Announcements
    • Thread Starter
    Offline

    1
    ReputationRep:
    Hi guys, I'm doing my C3 calculus work and I'm stuck on a question, it goes:

    Integrate: x(4-3x^2)^1/2 and give your answer as a fraction.

    I'm struggling to decide how to go about this, we've recently learnt integration by parts and integration by substitution - I'm not sure what will be easiest to do :')
    If you could talk me through what you're doing that would be extremely helpful - thanks all!!
    Offline

    16
    ReputationRep:
    Well it might be easiest to take x as U and (4-3x^2)^-1/2 as dV/dx since then dU/dx will equal 1 which is nice to have

    Integrate dV/dx to get V by letting 4-3x^2 = P so then you have to integrate P^-1/2.dx (remember to get dx in terms of dP so you can integrate)

    Posted from TSR Mobile
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by eternaforest)
    Well it might be easiest to take x as U and (4-3x^2)^-1/2 as dV/dx since then dU/dx will equal 1 which is nice to have

    Posted from TSR Mobile
    I've tried this but I think I must be integrating (4-3x^2)^1/2 wrong, do you know what v would be equal to?
    Offline

    16
    ReputationRep:
    (Original post by VetStudentOf2017)
    I've tried this but I think I must be integrating (4-3x^2)^1/2 wrong, do you know what v would be equal to?
    I edited my post, see if the extra bit helps

    Posted from TSR Mobile
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by eternaforest)
    I edited my post, see if the extra bit helps

    Posted from TSR Mobile
    That makes sense, thank you I'll give it a try!
    Offline

    16
    ReputationRep:
    (Original post by VetStudentOf2017)
    That makes sense, thank you I'll give it a try!
    How did it go?

    Posted from TSR Mobile
    Offline

    15
    ReputationRep:
    You can do this integral by inspection, or the reverse chain rule. Consider what the derivative of (4-3x^2)^3/2 is and then see how this relates to the integral.
    • Thread Starter
    Offline

    1
    ReputationRep:
    Hi guys!
    Sorry it took me so long to update on this, I was having problems accessing the post for some reason

    In the end I integrated by inspection as B_9710 said.

    u = 4-3x^2 and -1/3du = xdx

    so in the end it was -1/6 multiplied by the integral of u^1/2 and I substituted my limits in. I found the correct answer eventually which was 7/9! Thanks for your help
 
 
 
  • 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
    Should Spain allow Catalonia to declare independence?
    Help with your A-levels

    All the essentials

    The adventure begins mug

    Student life: what to expect

    What it's really like going to uni

    Rosette

    Essay expert

    Learn to write like a pro with our ultimate essay guide.

    Uni match

    Uni match

    Our tool will help you find the perfect course for you

    Study planner

    Create a study plan

    Get your head around what you need to do and when with the study planner tool.

    Study planner

    Resources by subject

    Everything from mind maps to class notes.

    Hands typing

    Degrees without fees

    Discover more about degree-level apprenticeships.

    A student doing homework

    Study tips from A* students

    Students who got top grades in their A-levels share their secrets

    Study help links and info

    Can you help? Study help unanswered threadsRules and posting guidelines

    Sponsored content:

    HEAR

    HEAR

    Find out how a Higher Education Achievement Report can help you prove your achievements.

    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.