Results are out! Find what you Get quick advice or join the chat
Hey! Sign in to get help with your study questionsNew here? Join for free to post

Core Maths 3: How do you integrate this?

Announcements Posted on
Review your Uni: we’re almost at 10,000 reviews. Our 10,000th will win £100 amazon voucher! 21-09-2015
  1. Offline

    Hi there

    I have the question:

    \displaystyle \int sin \frac{x}{3} dx

    I know that sin x integrated is - cos x,

    so is the answer to my question, before working out the exact values with the limits, this;

    \displaystyle - cos \frac{x}{3} + c

    Many thanks
  2. Offline

    The integral of sin(ax+b) is -(1/a)cos(ax+b).
    That means in this situation a is 1/3.
  3. Offline

    ok so in my case its -3 cos x ??
  4. Offline

    The x value must remain the same as 'a' remains in front it.
  5. Offline

    so its -3 cos 1/3x which is - cos x??
  6. Offline

    Yes and no. Cos(ax) is one value and 'a' cannot be changed by the value cos is multiplied by. The answer is -3cos(x/3). There's also a '+ c' but you already knew that. :P
  7. Offline

    ok thank you very much
  8. Offline

    (Original post by jackie11)
    ok thank you very much
    No problem; thanks for the rep.
  9. Offline

    I would suggest using the substitution method.
     \frac{x}{3} = u therefore \frac{du}{dx} = \frac{1}{3} so dx = 3 du

    The original equation is  \displaystyle \int sin \frac{x}{3}dx if you put in all the substituions you should get
     \displaystyle \int sin u 3du
    which simplifies to  \displaystyle 3 \int sin u du

    This should be fine to solve and then replace u with x/3 to get the final answer.


Submit reply


Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: April 17, 2012
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Today on TSR

You know you're a student when...

What's your defining moment?

What personality type are you?
Study resources
Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.