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Finding the total area between the curve and x axis

  1. Jan 25, 2012 #1

    jtt

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    1. The problem statement, all variables and given/known data
    find the total area of the region between the curve and the x- axis


    2. Relevant equations
    1) y=2-x, 0≤x≤3
    2)y=3x^2-3,-2≤x≤2
    3)y=x^3-3x^2+2x, 0≤x≤2
    4)y= x^3-4x, -2≤x≤2


    3. The attempt at a solution

    I've tried using my graphic calculator to see what the graphs looked like then i copied some of the points off of the table of x and y values so i could hand draw what i saw on the calculator. i'm completely stumped because i don't know if finding the total area for question 1 will be the same for the rest of the problems because it is a straight line not a curve. i am also getting net area confused with total area and don't know the difference between the 2. what about using the Riemann sums or trapezoidal rule? would i have to use it in order to solve these problems?
     
  2. jcsd
  3. Jan 25, 2012 #2

    Char. Limit

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    Gold Member

    Net area is the area above the x-axis, subtracting the area below the x-axis. The total area is the area above the x-axis, adding the area below the x-axis. In essence, the net area of f(x) from a to b is

    [tex]\int_a^b f(x) dx[/tex]

    While the total area of f(x) from a to b is

    [tex]\int_a^b |f(x)| dx[/tex]

    Hopefully that'll help.
     
  4. Jan 26, 2012 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    This is two right triangles. One with height 2 and base 2, the other with height 1 and base 1.

    3x^2- 3= 0 is the same as 3x^2= 3. Can you solve that?

    y= x(x^2- 3x+ 2)= 0 has x= 0 as one root and x^2- 3x+ 2= 0 is easily solvable.

    y= x(x^2- 4)= 0 has x-= 90 as one root and x^2- 4-= 0 is easily solvable.


     
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