# Area Under a Curve & Definite Integrals with TI NSPIRE Calculus 1 AB

CAS… and I want to do this in the same way
so you could do this on a TI-83 or a TI-84. We are going to go to ScratchPad and get the
graphing up. We already have the entry window open and our graph was 4x +12. Hit enter.
Hit the tab button again to open up that entry line and we have x^3, hit the arrow to get
the exponent, plus 3x^2. Enter. Alright. Well I can’t see the intersection of these 2
graphs, I am going to go to Menu, go to Window/Zoom and do Window settings. We are just going
to close up that window a little bit, maybe -7 and x max of +7 and we went low enough.
Let’s set y max be 24. And there we go. Now we are going to find both of the areas.
If you understand one, you can do both. So let’s find the bigger area here. Now we’re
going to find the area below the linear function and between the intersection points of -2
and +2. And then we are going to do the same thing with the cubic function and then subtract
them. So first, we are going to need to find the intersection point, assuming we don’t
already have them with us. So we are going to go to Menu – Analyze graph- find the
intersection. The calculator will ask you for the lower and upper bound, I am using
my touch pad of course but you will be using this pad here on your calculator and there
our intersection of (-2, 4) And then finally again, …. Menu – Analyze graph , using
touchpad, find the intersection- Lower bound and upper bound and there is the other intersection
point of (2, 20). Alright so, I want to find the area below the linear function of 4x +12
between these values. Menu-Analyze graph – let’s find the integral. The calculator will ask
you what graph. We want to do this one, so we got to do this one graph at a time. Lower
bound – you can just type in the number so I am going to go -2 and there is a little
box opening up here. Enter and you will see that actually with, the INSPIRE will show
me the area as I move my upper bound around. But I want to get that set to a concrete value
of 2 so I am just going to hit 2. There is a little window opening up for me and we have
that area of 48. I am going to write that down on my piece of paper. Now we are going
to find the area below the cubic function. So again Menu- Analyze graph- integral- which
graph. Well I want to use the cubic one this time. Lower bound -2 I am using my key board
here, but you will be hitting negative here and enter. Lock that up. Upper bound, I want
to again have that to be a value of 2. So I will just hit 2 and enter and the area below
the cubic function between that and the x axis was 16. And if you subtract those 48-16
is an area of 32 which was almost the complete answer I believe…the area between those
two graphs because this is just a small area. Now this is a CAS version which stands for
Computer Algebra System.  I could come over here to the, hit the tab button to toggle
between the two views, I could go to Menu- Calculus- Integral, my lower bound again was
-2 my upper bound was +2 and here I can just get the answer of 32. Hopefully get the same
answer. And actually I can type in the subtraction of those two function, now again the linear
function was first which was 4x +12 , minus, the other function has a lot of terms in it
so I am going to use parentheses . That cubic function was x^3 +3x^2. And we are going to
integrate that with respect to x. And voilà, we have 32 again. Now that was just one of
the two areas, you have to find the other one with a similar fashion and add those two
together to get the answer that I got in my video. Alright… thank you for watching.
Now let’s get back on to the next example.

### 14 thoughts on “Area Under a Curve & Definite Integrals with TI NSPIRE Calculus 1 AB”

• January 19, 2014 at 9:41 pm

Great stuff professor! Thanks!

• January 23, 2014 at 2:50 am

The AP Calculus BC test is almost here (May 7) and I noticed that your calculus playlist doesn't have a video covering polar curves. It's never too early to start preparing and I really enjoy how you thoroughly explain how to solve problems and I was wondering if you could please make a video that covers polar curves. Thank you!

• February 3, 2014 at 2:18 pm

I am impressed once again. Would love to see more Nspire example of Calculus AB topics. You might already have them. I will search. However, these will be added to the video list for my class.
R.O.

• April 10, 2014 at 5:37 pm

Hello, I am in college and I have the Ti-Nspire, and unfortunately all my professors know how to use the ti-84 and have NO IDEA how to use the Ti-Nspire I was required to have in high school. I REALLY APPRECIATE these videos you are putting up! It's very frustrating trying to do stuff in my calc classes with too fancy of a calculator. Thank you so much!

• May 7, 2014 at 10:15 pm

I know there is a rectangle program that does Reimann Sums on the TI84. I tried to find a program that does something similar on the CX, but I've not been able to figure it out. Do you know if it's possible to run something like the (b-a)/n xi summation for left, right and midpoints? Thanks!

• June 3, 2014 at 9:12 am

Hi! How would you graph in terms of Y? my graphs do not show up

• September 16, 2014 at 11:51 am

Hello sir! My nspire calculator doesn't seem to have a box where I can put exact numbers where I want to start to find the area. In your video, you could simply put the value of -2 with thee number pad; however, I do not have that. So, when it comes to decimals, I can't find the area under the curve by using my nspire calculator because there is no box that seem to appear where I can easily type the number I want to start in the lower bound section. Im so fraustrated 🙁 Can you help me?

• April 2, 2015 at 1:29 am

Texas Instruments, thanks all!

• September 4, 2015 at 1:28 am

how converter number para trigonometry form
0,707 = sen(45)

• August 20, 2016 at 12:33 am

Can you graph in terms of y? for example my book has y=x^2 and y=x^3 but i cant figure out how to graph it. P.S i need to be able to graph the function so i can tell which equation is my upper and lower bounds on more complicated equations

• September 25, 2016 at 7:22 pm

if you select both graphs then drag, it will get you the area. what you did was way harder

• April 26, 2017 at 1:05 pm

Thank you. Very clear.