Results 1 to 7 of 7

Math Help - Is this me or the book?

  1. #1
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1

    Is this me or the book?

    I am doing a question on finding the area enclosed by a loop, given by the equation:

    r = 2\cos^{\frac{3}{2}}\theta with \frac{-\pi}{2} \le\theta\le \frac{\pi}{2}.

    I know that the area is \frac{1}{2} \int r^2 d\theta

    Which works out to be \frac{1}{2} \int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} 4\cos^{3}\theta  d\theta

    Taking out the 4 and expanding I end up with 2 \int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \cos{\theta}(1-\sin^{2}\theta) d\theta

    The book however has a 4 outside the brackets, is this a typo or something that I've missed?

    Thanks for the help
    Last edited by craig; May 27th 2009 at 02:35 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member apcalculus's Avatar
    Joined
    Apr 2009
    From
    Boston
    Posts
    293
    I would have done the same as what you have; could the lower bound at the very last step have been changed in the book from -pi/2 to 0, which would then require to double the integral in order to get the full loop?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    000
    000 is offline
    Newbie
    Joined
    Aug 2008
    Posts
    8
    hey isnt it from -pi/2 to +pi/2 ??? how come it became -pi/2 to 1/pi ???
    if its from -pi/2 to +pi/2 then u will have 4 outside... and integral will become from 0 to +pi/2....
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1
    Quote Originally Posted by 000 View Post
    hey isnt it from -pi/2 to +pi/2 ??? how come it became -pi/2 to 1/pi ???
    if its from -pi/2 to +pi/2 then u will have 4 outside... and integral will become from 0 to +pi/2....
    Sorry that was a typo on my part, the limits are \frac{-\pi}{2} \le \theta \le \frac{\pi}{2} .

    Could you explain why it becomes 4 outside, sorry I don't quite understand?

    Thanks for the replies
    Follow Math Help Forum on Facebook and Google+

  5. #5
    000
    000 is offline
    Newbie
    Joined
    Aug 2008
    Posts
    8
    hey  \cos^3{\theta} is an even function... so integral from -\pi/2 to  +\pi/2 becomes twice integral 0 to  +\pi/2

    Since The integral of an even function from −A to +A is twice the integral from 0 to +A

    hence u get four outside....
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1
    Of course do you!!! Does anyone else fail to see the blindingly obvious when doing complicated maths lol?

    Thanks for the help
    Follow Math Help Forum on Facebook and Google+

  7. #7
    000
    000 is offline
    Newbie
    Joined
    Aug 2008
    Posts
    8
    hehe... thats called carelessness.... I am a master at making these type of mistakes... hope i dont make any for tommorows university exam...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Do you have this book??
    Posted in the Business Math Forum
    Replies: 6
    Last Post: September 14th 2010, 07:05 PM
  2. i need this book
    Posted in the Differential Geometry Forum
    Replies: 13
    Last Post: July 26th 2009, 05:35 AM
  3. Book vs. me ---- who is right?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 15th 2009, 11:38 AM

Search Tags


/mathhelpforum @mathhelpforum