# Math Help - using a graphics calculator to find an area of two functions and integration

1. ## using a graphics calculator to find an area of two functions and integration

Hi,
I have a question that I would appreciate some help with.

I need to use my graphics calculator to find the area bound by y=x ^3 - 2x- 5x +3 and y=x ^2 -2x-3. Then I need to draw a diagram to illustrate the area and show details of how I arrived at my answer using my calculator.

I figured out what I believe are to be the first few steps, which I will write below. However, I am not aware of what I should do next.

1) Enter the function x ^3 - 2x- 5x +3 as Y=1 in the Y= menu and enter the function x ^2 -2x-3 as Y=2 in the Y= menu
2) Press Graph
3) Press trace and find the parts of the intersection of both graphs
4) I am pretty sure the points are (-1.49, 2.58) (1.06, 3.87) (3.4, 1.29)

So any help possible would be great.

Then for the question after that I need to use integration techniques to find the same area from the above question. So if you could help at all with that as well it would be most appreciated.

thankyou

2. Originally Posted by needmathshelp
Hi,
I have a question that I would appreciate some help with.

I need to use my graphics calculator to find the area bound by y=x ^3 - 2x- 5x +3 and y=x ^2 -2x-3. Then I need to draw a diagram to illustrate the area and show details of how I arrived at my answer using my calculator.

I figured out what I believe are to be the first few steps, which I will write below. However, I am not aware of what I should do next.

1) Enter the function x ^3 - 2x- 5x +3 as Y=1 in the Y= menu and enter the function x ^2 -2x-3 as Y=2 in the Y= menu
2) Press Graph
3) Press trace and find the parts of the intersection of both graphs
4) I am pretty sure the points are (-1.49, 2.58) (1.06, 3.87) (3.4, 1.29)

So any help possible would be great.

Then for the question after that I need to use integration techniques to find the same area from the above question. So if you could help at all with that as well it would be most appreciated.

thankyou
Hello,

I assume that
- your 1st function reads: y1(x) = x ^3 - 2x^2- 5x +3
- you use a TI83 or TI84 (?). If not please tell me which calculator you use.

1. Draw the graphs as you have described. Then use CALC (=2ND TRACE) #5 to get the intersections of these graphs.

2. The area enclosed by two graphs is calculated by:

$a=\int_{lower~bound}^{upper~bound}(y1(x)-y2(x))dx$

So first calculate the difference of the two functions: $d(x) = x^3-3x^2-3x+6$

3. type at $y3(x) = \underbrace{abs(}_{from~catalog}x^3-3x^2-3x+6)$ and draw the graph. Switch off the 2 previous graphs.

4. Use TRACE #7 to calculate the area. Type in the bounds which you have calculated with the intersections.

I've attached an image which shows the complete work.