Page 2 of 2 FirstFirst 12
Results 16 to 28 of 28

Math Help - Area of 2 curves -Integration

  1. #16
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,879
    Thanks
    742

    Re: Area of 2 curves -Integration

    Quote Originally Posted by Darrylcwc View Post
    I contrast my set up with yours and I don't understand why the second set up ranges from 0,2. The point of intersection is at 0,3.
    That was actually my mistake. I had a smudge on my monitor and when I first read your post, I thought that the functions were:
    y=x^2, y=3x, x=-1, x=2

    I missed the negative sign before the two for the last line. It is sheer coincidence that the integrals I set up happen to yield the same answer as the one on your answer sheet.
    Follow Math Help Forum on Facebook and Google+

  2. #17
    Senior Member
    Joined
    Sep 2013
    From
    USA
    Posts
    255
    Thanks
    114

    Re: Area of 2 curves -Integration

    Here's what I did:
    Area of 2 curves -Integration-untitled2.gif

    this is not 31/6. Either the answer in your sheet is incorrect, or you posted the limits incorrectly.
    Follow Math Help Forum on Facebook and Google+

  3. #18
    Junior Member
    Joined
    Oct 2013
    From
    Australia
    Posts
    45

    Re: Area of 2 curves -Integration

    I got 41/6. But the answer states 31/6!
    This is shouldn't to be, by virtue, a straight to the point simple problem because of the abstraction. I don't fare very well in applicational calculus.
    However, it's ridiculous that I'm always working out 41/6 but which the sheet states 31/6.

    I typed the question word for word.
    Follow Math Help Forum on Facebook and Google+

  4. #19
    Senior Member
    Joined
    Sep 2013
    From
    USA
    Posts
    255
    Thanks
    114

    Re: Area of 2 curves -Integration

    Quote Originally Posted by Darrylcwc View Post
    I got 41/6. But the answer states 31/6!
    This is shouldn't to be, by virtue, a straight to the point simple problem because of the abstraction. I don't fare very well in applicational calculus.
    However, it's ridiculous that I'm always working out 41/6 but which the sheet states 31/6.

    I typed the question word for word.
    I am sorry to tell you the answer in your sheet is incorrect. It is not the answer to the question.
    Follow Math Help Forum on Facebook and Google+

  5. #20
    Junior Member
    Joined
    Oct 2013
    From
    Australia
    Posts
    45

    Re: Area of 2 curves -Integration

    Quote Originally Posted by votan View Post
    I am sorry to tell you the answer in your sheet is incorrect. It is not the answer to the question.
    I'm already starting to suspect that I have wasted almost 2 days working out the other same problems over and over again because of wrong answers where in fact the sheet is flawed.
    Follow Math Help Forum on Facebook and Google+

  6. #21
    Junior Member
    Joined
    Oct 2013
    From
    Australia
    Posts
    45

    Re: Area of 2 curves -Integration

    Quote Originally Posted by Darrylcwc View Post
    I'm already starting to suspect that I have wasted almost 2 days working out the other same problems over and over again because of wrong answers where in fact the sheet is flawed.

    wait, something isn't right.
    The answer ought to be 41/6 - 9/2. Why does your set up consist only of a x^2? It should be x^2-3x for int -1 to -2; and, 3x-x^2 for int 0 to 3;
    Follow Math Help Forum on Facebook and Google+

  7. #22
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,879
    Thanks
    742

    Re: Area of 2 curves -Integration

    You always integrate from left to right. That is how the definite integral is defined. If you integrate from right to left, you get negative the correct area.

    So, if you integrate from -1 to -2, you are integrating from a bigger number to a smaller number. That is going right to left. You mean it should be the integral of x^2-3x from -2 to -1? Yes. That is correct.

    The region bounded by y=3x and y=x^2 from x=0 to x=3 is NOT part of the region bounded by
    y=x^2, y=3x, x=-2, and x=-1

    Note that x=0 and x=3 are both bigger than x=-1, which is the right bound of the two lines (x=-2 and x=-1). So, if you include that area, you are included area that is NOT bounded by the given functions and lines.
    Follow Math Help Forum on Facebook and Google+

  8. #23
    Junior Member
    Joined
    Oct 2013
    From
    Australia
    Posts
    45

    Re: Area of 2 curves -Integration

    We might be confused by a case of semantics or stipulative definition.
    Shouldn't the bigger value be at the top of the sigma?

    Edit: In essence, if I move along the x-axis from right to left, I would obtain a negative value-small value minus larger value. So therefore, adding a minus sign outside of the sigma resolve this problem since area can never be negative much like a scalar value.
    In moving from left to right, we would proceed the algebraic operation as per usual since we will always obtain a positive value
    Last edited by Darrylcwc; October 9th 2013 at 08:25 AM.
    Follow Math Help Forum on Facebook and Google+

  9. #24
    Junior Member
    Joined
    Oct 2013
    From
    Australia
    Posts
    45

    Re: Area of 2 curves -Integration

    On a tangent:
    How should I deal with a function where f'(x) = ln(x) to be integrate along the x-axis from positive to negative and negative to positive?
    Follow Math Help Forum on Facebook and Google+

  10. #25
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,879
    Thanks
    742

    Re: Area of 2 curves -Integration

    Use integration by parts
    Follow Math Help Forum on Facebook and Google+

  11. #26
    Senior Member
    Joined
    Sep 2013
    From
    USA
    Posts
    255
    Thanks
    114

    Re: Area of 2 curves -Integration

    Quote Originally Posted by Darrylcwc View Post
    We might be confused by a case of semantics or stipulative definition.
    Shouldn't the bigger value be at the top of the sigma?
    That's correct, -1 is begger than -2
    Follow Math Help Forum on Facebook and Google+

  12. #27
    Senior Member
    Joined
    Sep 2013
    From
    USA
    Posts
    255
    Thanks
    114

    Re: Area of 2 curves -Integration

    Quote Originally Posted by Darrylcwc View Post
    On a tangent:
    How should I deal with a function where f'(x) = ln(x) to be integrate along the x-axis from positive to negative and negative to positive?
    Please post this in a different thread and give it a new title. Thanks
    Follow Math Help Forum on Facebook and Google+

  13. #28
    Senior Member
    Joined
    Sep 2013
    From
    USA
    Posts
    255
    Thanks
    114

    Re: Area of 2 curves -Integration

    Quote Originally Posted by Darrylcwc View Post
    wait, something isn't right.
    The answer ought to be 41/6 - 9/2. Why does your set up consist only of a x^2? It should be x^2-3x for int -1 to -2; and, 3x-x^2 for int 0 to 3;
    You could verity the validity of the answer this way.

    Consider the trpezoid bouded but small base 1 +3 = 4 these are the coordinates from the parabola and the line. It is +3 because we are using the distance between points.

    The long base is 4 + 6 = 10

    area = [(10 + 4)/2]*1 = 7 = 42/6

    This area is slightly larger than 41/6 because the curvature of the pararable
    Follow Math Help Forum on Facebook and Google+

Page 2 of 2 FirstFirst 12

Similar Math Help Forum Discussions

  1. Integration: Area under curves
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 27th 2010, 01:52 AM
  2. area between curves w/ integration by parts
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 11th 2010, 04:17 PM
  3. Integration- Area under curves
    Posted in the Calculus Forum
    Replies: 6
    Last Post: July 13th 2009, 01:16 PM
  4. Area under two curves by integration
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 7th 2007, 07:45 AM
  5. Area between curves (integration)
    Posted in the Calculus Forum
    Replies: 10
    Last Post: June 9th 2007, 04:53 PM

Search Tags


/mathhelpforum @mathhelpforum