Finding the total area between the curve and x axis

  • Thread starter jtt
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  • #1
jtt
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Homework Statement


find the total area of the region between the curve and the x- axis


Homework 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


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?
 

Answers and Replies

  • #2
Char. Limit
Gold Member
1,208
14
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.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,847
966

Homework Statement


find the total area of the region between the curve and the x- axis


Homework Equations


1) y=2-x, 0≤x≤3
This is two right triangles. One with height 2 and base 2, the other with height 1 and base 1.

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

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

4)y= x^3-4x, -2≤x≤2
y= x(x^2- 4)= 0 has x-= 90 as one root and x^2- 4-= 0 is easily solvable.


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?
 

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