Page 1 of 2 12 LastLast
Results 1 to 15 of 26

Math Help - Area under a curve

  1. #1
    Member
    Joined
    Feb 2010
    From
    United States
    Posts
    155
    Thanks
    1

    Area under a curve

    Find the area under the graph to the x axis from -2 to 2 for

    f(x) = (4 - x^2)^(1/2)


    Okay, so I understand how to do the problem overall but I don't know how to take the antiderivative of that particular function. Is there an easy way to do the chain rule in reverse or what...
    Last edited by bobsanchez; August 6th 2010 at 01:05 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Is that f(x)=\sqrt{4-x^{2}}? If so, I wouldn't integrate. You can solve the problem without integrating. Think about what the shape of that curve is.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2010
    From
    United States
    Posts
    155
    Thanks
    1
    Yeah, that's the function. It's a semicircle?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    It's a semicircle?
    Show me that it's a semicircle.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Feb 2010
    From
    United States
    Posts
    155
    Thanks
    1
    It just is. What do you mean?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    I asked my question because you seemed unsure of whether it's a semicircle or not. If you are sure, then what do you get for the area under it?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Feb 2010
    From
    United States
    Posts
    155
    Thanks
    1
    Oh, sorry. I had the question mark there because I didn't know where you were going with it, not whether or not it's a semicircle. Um...I don't really know. It's doesn't quite touch the x-axis according to my graphing calculator, and as a result it is sort of messing with all of the estimations I've attempted, and I don't know how to integrate a function like that.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Are you required to solve this problem using integration? Because I find that simply writing the answer down is a lot easier. What's the radius of this semicircle? And what's the area of a semicircle in general?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member 11rdc11's Avatar
    Joined
    Jul 2007
    From
    New Orleans
    Posts
    894
    Follow Ackbeet's advice. Integration is just the area under the curve so...
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Member
    Joined
    Feb 2010
    From
    United States
    Posts
    155
    Thanks
    1
    I think integration is preferred, but this method should suffice.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    And the answer is ...
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Member
    Joined
    Feb 2010
    From
    United States
    Posts
    155
    Thanks
    1
    6.28
    Follow Math Help Forum on Facebook and Google+

  13. #13
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Or, more accurately, 2\pi.
    Follow Math Help Forum on Facebook and Google+

  14. #14
    Member
    Joined
    Feb 2010
    From
    United States
    Posts
    155
    Thanks
    1
    Touche, but it was supposed to be rounded to two decimal places, so I had to.
    Follow Math Help Forum on Facebook and Google+

  15. #15
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Then 6.28 might not be the more accurate answer, but it is the better answer. In engineering, at least, you better give an answer that your boss is happy with. If he wants decimals, give him decimals. Otherwise, it won't be as useful to him.
    Follow Math Help Forum on Facebook and Google+

Page 1 of 2 12 LastLast

Similar Math Help Forum Discussions

  1. AREA under the curve
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 27th 2010, 11:39 PM
  2. Area under a curve
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 29th 2009, 11:52 AM
  3. Area under the curve
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 18th 2009, 11:34 AM
  4. Area below a curve
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 14th 2008, 09:43 AM
  5. area under the curve
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 31st 2007, 02:22 PM

Search Tags


/mathhelpforum @mathhelpforum