A Second Line Example


In this second example, we will find the area under the line y = 2.5 - x from x = 0 to x = 5.   This is a little trickier than the first example since there is a positive area and a negative area that we need to add together.   This is the same as

We'll be using the "Area" tool so bring that window up.  

Graph the curve y = 2.5 - x in the "Area" tool.

This time we'll use a triangle as our geometric shape.   And we'll need to do 2 calculations:

  1. One to calculate the positive area which is from x = 0 to x = 2.5, and
  2. another to calculate the negative area which is from x = 2.5 to x = 5.
Then we'll account for the negative area by subtracting the area we got for x = 2.5 to x = 5 from the area we got for x = 0 to x = 2.5.

The steps are:

  1. Drop a triangle down, resize it to fit between the curve and the x-axis from x = 0 to x = 2.5, and then calculate (and record) this area.   Call this area A1.
  2. Now drag and resize the triangle to fit the area between the x-axis and the line from x = 2.5 to x = 5, and then calculate (and record) this area.   Call this area A2.

Then the area under the line from x = 0 to x = 5 is A1 - A2.   Your answer for A1 - A2 should be very close to 0 since we know that






Next: Follow the "A Curve" link.