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Math Help - The Area Between Two Curves

  1. #1
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    The Area Between Two Curves

    Can someone please help me?

    Find the area between y= 2-3x^2, y=6, x=1, x=5
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  2. #2
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    Quote Originally Posted by McDiesel View Post
    Can someone please help me?

    Find the area between y= 2-3x^2, y=6, x=1, x=5
    Quite unclear on what you just typed. Type it exactly from your homework.


    If you type what I think it is, then solve this eqn.
    \int\limits_1^5 {(6 - 2+ 3x^2)} dx
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  3. #3
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    yeah, thats the right equation but shouldn't it be -3x^2? I worked the equation out and I get -140 but the answer is 140...not sure why
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  4. #4
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    Quote Originally Posted by McDiesel View Post
    yeah, thats the right equation but shouldn't it be -3x^2? I worked the equation out and I get -140 but the answer is 140...not sure why
    Nope, because the area under the curve of -3x^2 is negative. And you are trying to find the total absolute area between two curves. Therefore (2-3x^2) becomes (-2+3x^2)

    if you get a negative answer, that means your answer is wrong.

    \int\limits_1^5 {(6 - 2+ 3x^2)} dx = 140 NOT -140

    140 is the total area between the two curves, since the area under the x-axis is negative so you have to take into account for that.
    Last edited by TitaniumX; November 17th 2008 at 11:25 AM.
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  5. #5
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    Here is my work, where did I go wrong?

    \int\limits_1^5 {(6-2-3x^2)}

    2x-(3x^3/3)-6x

    2x-x^3-6x

    2(5)-5^3-6(5)-[2(1)-1^3-6(1)]

    =-140

    So where did I go wrong?
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  6. #6
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    Quote Originally Posted by McDiesel View Post
    Here is my work, where did I go wrong?

    \int\limits_1^5 {(6-2+3x^2)}

    2x-(3x^3/3)-6x

    2x-x^3-6x

    2(5)-5^3-6(5)-[2(1)-1^3-6(1)]

    =-140

    So where did I go wrong?
    You signs are messed up. The first step... 2x should be -2x and -6x and be 6x.

    Remember that you have to change the signs of the (2-3x^2) to (-2+3x^2)
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  7. #7
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    Here, I just edited your steps

    \int\limits_1^5 {(6-2-3x^2)}dx

    = \int\limits_1^5 {(4-3x^2)}dx

    4x+(3x^3/3)

    4x+x^3

    [4(5)+5^3]- [4(1)+(1)^3]

    [145]- [5]

    =140
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  8. #8
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    Quote Originally Posted by McDiesel View Post
    yeah, thats the right equation but shouldn't it be -3x^2? I worked the equation out and I get -140 but the answer is 140...not sure why
    Draw a picture, it will make it clear what area the problem is asking for.

    CB
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