Results 1 to 8 of 8

Math Help - find area integration

  1. #1
    Super Member
    Joined
    Oct 2007
    From
    Santiago
    Posts
    517

    find area integration

    find the area between the graph of y= 6x^2 - 42x + 60 and the x-axis, between x=1 and x=4.

    any ideas? thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by jvignacio View Post
    find the area between the graph of y= 6x^2 - 42x + 60 and the x-axis, between x=1 and x=4.

    any ideas? thank you
    Draw a graph and it should be clear that you need to consider two seperate integrals:

    1. \int_1^2 6x^2 - 42x + 60 \, dx.

    2. \left| \int_2^4 6x^2 - 42x + 60 \, dx \right|.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Oct 2007
    From
    Santiago
    Posts
    517
    Quote Originally Posted by mr fantastic View Post
    Draw a graph and it should be clear that you need to consider two seperate integrals:

    1. \int_1^2 6x^2 - 42x + 60 \, dx.

    2. \left| \int_2^4 6x^2 - 42x + 60 \, dx \right|.
    for the graph should i just plug in some values for x then get points for y? being an absolute intergration does it make a difference?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by jvignacio View Post
    for the graph should i just plug in some values for x then get points for y? being an absolute integer does it make a difference?
    If you're studying integral calculus you should know how to draw the graph of a parabola. Especially one whose equation factorises so easily.

    I don't know what you mean by absolute integer?
    means take the magnitude of the integral (since the integral itself is negative).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Oct 2007
    From
    Santiago
    Posts
    517
    Quote Originally Posted by mr fantastic View Post
    If you're studying integral calculus you should know how to draw the graph of a parabola. Especially one whose equation factorises so easily.

    I don't know what you mean by absolute integer?
    means take the magnitude of the integral (since the integral itself is negative).
    \int_1^2 6x^2 - 42x + 60 dx + \int_2^4 6x^2 - 42x + 60 dx


    i got -9 for my final answer?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by jvignacio View Post
    \int_1^2 6x^2 - 42x + 60 dx + \int_2^4 6x^2 - 42x + 60 dx


    i got -9 for my final answer?
    How can an area between the curve and the x-axis be negative?

    The answer has to be positive. Did you draw the graph?

    It looks like you haven't taken the magnitude of \int_2^4 6x^2 - 42x + 60 \, dx like I said to. But without seeing th details of your calculation it's impossible to know for sure what mistakes you have made.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member
    Joined
    Oct 2007
    From
    Santiago
    Posts
    517
    Quote Originally Posted by mr fantastic View Post
    How can an area between the curve and the x-axis be negative?

    The answer has to be positive. Did you draw the graph?

    It looks like you haven't taken the magnitude of \int_2^4 6x^2 - 42x + 60 \, dx like I said to. But without seeing th details of your calculation it's impossible to know for sure what mistakes you have made.
    when i integrated \int_2^4 6x^2 - 42x + 60 \, dx that gave me a -20.. so hence my result being a negative but when u say magnitude, what do this mean?

    do i need to change the all the signs to its opposite .. - = + and + = - ?

    that gives me 31
    Last edited by jvignacio; November 12th 2008 at 01:10 PM.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by jvignacio View Post
    when i integrated \int_2^4 6x^2 - 42x + 60 \, dx that gave me a -20.. so hence my result being a negative but when u say magnitude, what do this mean?

    do i need to change the all the signs to its opposite .. - = + and + = - ?

    that gives me 31
    The magnitude of -20 is 20.

    So yes, 31 is the answer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Double integration to find area
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 5th 2010, 07:20 PM
  2. integration to find area please
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 5th 2009, 12:50 PM
  3. Double integration to find the area
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 5th 2009, 06:23 PM
  4. Integration - Find the area
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 5th 2008, 06:50 PM
  5. Integration to find a bound area
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 5th 2007, 02:29 PM

Search Tags


/mathhelpforum @mathhelpforum