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

Integration help (any help is better than none!) Watch

    • Thread Starter
    Offline

    8
    ReputationRep:
    I'm only asking this here because I can't think of anyone else I can possibly ask, so hopefully someone can help me.
    I always thought I was good at maths, but obviously not.

    Anyway, there are two questions I'm struggling with.

    1)Evaluate∫(cosπx/2)dx with limits from 0-1

    2) Evaluate
    ∫dx/(x+1)^1/2 with limits from 0-3

    The first one has me completely lost, like I genuinely have no idea where to begin, we've never been shown anything like that in class.

    The second one has me a bit baffled, but also wondering if it's a typo or just another way of typing "with respect to x," however I've never seen it written with the dx as the numerator and everything else as the denominator.

    If anyone can help with anything, then you'd be a life saver because I'm about to crack my head off of a wall.
    Offline

    16
    ReputationRep:
    Is the first one

    \int \cos (\frac{\pi x}{2}) dx

    If so try differentiating \sin (\frac{\pi x}{2})
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by TenOfThem)
    Is the first one

    \int \cos (\frac{\pi x}{2}) dx

    If so try integrating \sin (\frac{\pi x}{2})
    Yeah that's the first one, although I'm going to make myself sound like an idiot here,
    1) how would integrating sin(πx/2) help with cos(πx/2)?
    and 2) I still don't know how I'd even go about doing that. It's the πx/2 that's throwing me off. I'm sure it's really simple once I know how, but my issue is that I don't know how to start with, haha. Urgh I feel so stupid trying to figure this out!
    Offline

    16
    ReputationRep:
    (Original post by angelooo)

    1) how would integrating sin(πx/2) help with cos(πx/2)?
    !
    ooops see edit
    Offline

    16
    ReputationRep:
    (Original post by angelooo)
    It's the πx/2 that's throwing me off.
    Can you do \int \cos (3x) dx as the method is the same
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by angelooo)
    Yeah that's the first one, although I'm going to make myself sound like an idiot here,
    1) how would integrating sin(πx/2) help with cos(πx/2)?
    and 2) I still don't know how I'd even go about doing that. It's the πx/2 that's throwing me off. I'm sure it's really simple once I know how, but my issue is that I don't know how to start with, haha. Urgh I feel so stupid trying to figure this out!
    \displaystyle \int \cos (ax+b) \, dx = \frac{\sin (ax+b)}{a}+k
    Offline

    0
    ReputationRep:
    For question 2, another way of writing that, which i find clearer would be

    1/ (x+1)^1/2 x dx

    then its been put into the form of any other integral you are used to?
    Hope that makes sense, i don't know how to do the integral signs etc :P
    Offline

    16
    ReputationRep:
    (Original post by TheHaylio)
    F

    1/ (x+1)^1/2 x dx
    Where does this x come from
    Offline

    0
    ReputationRep:
    (Original post by TenOfThem)
    Where does this x come from
    meant to be a multiplied sign sorry
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by TenOfThem)
    Can you do \int \cos (3x) dx as the method is the same
    Would that be 1/3sin3x+c?
    Sorry, I obviously have no idea how to insert equations here either.

    I know the chain rule for standard integrals, but I think the fraction is just throwing me a bit.

    cos (ax+b) dx = 1/a sin (ax+b) + x

    so in my problem, would a = πx? or would a = πx/2? or am I still totally wrong?

    Thanks for this btw!
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by TheHaylio)
    For question 2, another way of writing that, which i find clearer would be

    1/ (x+1)^1/2 x dx

    then its been put into the form of any other integral you are used to?
    Hope that makes sense, i don't know how to do the integral signs etc :P
    Yes that's exactly what I thought it meant, but I wasn't sure if it was a totally different problem or just another way of writing it. So let me get this right, even if the dx is a numerator to what I'm trying to integrate, it still means I'm just integrating it with respect to x, yeah?

    If that's right, then you've honestly just made my day hahaha
    Offline

    16
    ReputationRep:
    (Original post by angelooo)
    Would that be 1/3sin3x+c?
    Yes, essentially you just divide by the constant and in your question the constant will be \frac{\pi}{2}
    Offline

    16
    ReputationRep:
    (Original post by angelooo)
    Yes that's exactly what I thought it meant, but I wasn't sure if it was a totally different problem or just another way of writing it. So let me get this right, even if the dx is a numerator to what I'm trying to integrate, it still means I'm just integrating it with respect to x, yeah?

    If that's right, then you've honestly just made my day hahaha
    Yes

    \displaystyle \int \dfrac{dx}{f(x)} = \displaystyle \int \dfrac{1}{f(x)} dx
    Offline

    0
    ReputationRep:
    (Original post by angelooo)
    Yes that's exactly what I thought it meant, but I wasn't sure if it was a totally different problem or just another way of writing it. So let me get this right, even if the dx is a numerator to what I'm trying to integrate, it still means I'm just integrating it with respect to x, yeah?

    If that's right, then you've honestly just made my day hahaha
    Yep
    hhaha, good!
    Offline

    1
    ReputationRep:
    (Original post by TheHaylio)
    meant to be a multiplied sign sorry
    http://www.numberempire.com/texequat...tioneditor.php

    use that, it prevents ambiguous equations and saves time having to learning how to use latex

    just copy and paste the expression
    • Thread Starter
    Offline

    8
    ReputationRep:
    I wish I could give all a big cuddle or something to show my gratitude! I also wish I'd come here when I was first struggling for help because it would've saved a massive headache hahaha. Thanks so much everyone, you're all stars!
    Offline

    0
    ReputationRep:
    (Original post by TenOfThem)
    Yes

    \displaystyle \int \dfrac{dx}{f(x)} = \displaystyle \int \dfrac{1}{f(x)} dx
    Looks so much better with the symbals :P
    Offline

    0
    ReputationRep:
    (Original post by upthegunners)
    http://www.numberempire.com/texequat...tioneditor.php

    use that, it prevents ambiguous equations and saves time having to learning how to use latex

    just copy and paste the expression
    Thanks!
    Offline

    0
    ReputationRep:
    (Original post by angelooo)
    I wish I could give all a big cuddle or something to show my gratitude! I also wish I'd come here when I was first struggling for help because it would've saved a massive headache hahaha. Thanks so much everyone, you're all stars!
    Haha! Thats okay, i always end up asking for help here- it's good to be able to actually give some help back for once!
    Offline

    16
    ReputationRep:
    (Original post by angelooo)
    I wish I could give all a big cuddle or something to show my gratitude! I also wish I'd come here when I was first struggling for help because it would've saved a massive headache hahaha. Thanks so much everyone, you're all stars!
    NP

    :hugs:
 
 
 
  • 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
    Would you like to hibernate through the winter months?
    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.