Results 1 to 7 of 7

Math Help - Area of region

  1. #1
    Member
    Joined
    Aug 2011
    Posts
    117

    Area of region

    Basically, what i have is

    V = 2 \pi \int _{o}^ {4} (4-x) \, \sqrt x \, dx

    would i then distribute?


    V = 2 \pi \int _{o}^ {4} (4x^{1/2} -x ^{3/2} )  dx

    Then, integrate?

      2 \pi \int _{o}^ {4} (4 * \frac {2} {3} x^{3/2} - \frac {2}{5} x ^{5/2}

    then,


      2 \pi [  \frac {8} {3} x^{3/2} - \frac {2}{5} x ^{5/2}]
    evaluated from 0 to 4

    Is this correct? I cant seem to get a decent answer. Wolfram gives me weird steps and an answer i cant match...And when would i do something with the 2pi? Do i use 2pi for each side?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,130
    Thanks
    337

    Re: Area of region

    Quote Originally Posted by icelated View Post
      2 \pi [  \frac {8} {3} x^{3/2} - \frac {2}{5} x ^{5/2}]
    evaluated from 0 to 4

    Is this correct?
    Looks good so far. When you evaluate from 0 to 4 you should get:

     2 \pi [ (\frac 8 3 4 ^{3/2} - \frac 2 5 4^ {5/2} )-(0 - 0)] = \frac {256 \pi}{15}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Re: Area of region

    Quote Originally Posted by icelated View Post
    Basically, what i have is

    V = 2 \pi \int _{o}^ {4} (4-x) \, \sqrt x \, dx

    would i then distribute?


    V = 2 \pi \int _{o}^ {4} (4x^{1/2} -x ^{3/2} )  dx

    Then, integrate?

      2 \pi \int _{o}^ {4} (4 * \frac {2} {3} x^{3/2} - \frac {2}{5} x ^{5/2}

    then,


      2 \pi [  \frac {8} {3} x^{3/2} - \frac {2}{5} x ^{5/2}]
    evaluated from 0 to 4

    Is this correct? I cant seem to get a decent answer. Wolfram gives me weird steps and an answer i cant match...And when would i do something with the 2pi? Do i use 2pi for each side?


    umm if you evaluate the last line that you have from 0 to 4 you will get the correct answer! Does W.A give you  \frac{256}{15}\pi?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Aug 2011
    Posts
    117

    Re: Area of region

    yeah, thats the answer but i cant seem to get that. Does the 2pi get times by both sides after i fill in 4 for x?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Re: Area of region

    Quote Originally Posted by icelated View Post
      2 \pi [  \frac {8} {3} x^{3/2} - \frac {2}{5} x ^{5/2}]
    This means

     2 \pi [  \frac {8} {3} x^{3/2} - \frac {2}{5} x ^{5/2}] \bigg|_{0}^{4} =2\pi\left[ \frac{8}{3}4^{3/2}-\frac{2}{5}4^{5/2}-\left(  \frac{8}{3}0^{3/2}-\frac{2}{5}0^{5/2}\right) \right]

    Now just use algebra to simplify
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Aug 2011
    Posts
    117

    Re: Area of region

    That answers my questions thank you. Do i need to do anything to the thread?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2

    Re: Area of region

    Quote Originally Posted by icelated View Post
    Do i need to do anything to the thread?
    Nope. We don't generally close threads around here unless there's been a violation of rules. Although, come to think of it, if you like, you can mark the thread as solved. That's in the "Thread Tools" menu.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Area of region.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 11th 2009, 01:30 PM
  2. Area of region
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 27th 2009, 03:46 AM
  3. Area of the region?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 12th 2009, 08:10 AM
  4. Help with area of region
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 3rd 2008, 01:55 AM
  5. Area of a region
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 18th 2006, 11:56 PM

/mathhelpforum @mathhelpforum