Finding the total area between the curve and x axis

[jtt]

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?

 

[Char. Limit]

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

$$\int_a^b f(x) dx$$

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

$$\int_a^b |f(x)| dx$$

Hopefully that'll help.

 

[HallsofIvy]

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?