2. Fundamental Theorem of Calculus using the TiNspire – Step by Step

Applying the Fundamental Theorem of Calculus using the TiNspire – Step by Step – can easily be done using Calculus Made Easy at www.TiNspireapps.com . Here is an example:

Just enter the given function f(t) which is the integrand.

Next, enter the upper bound of the given definite integral.

Then , Calculus Made Easy provides you with the Theorem and also applies it to show the correct answer.

Steps for the computation can be seen below: First the integrand is integrated and evaluated using the given bounds . Lastly, differentiation yields that final answer.

TiNspire : Volume of Solids of Revolution using Disk, Washer and Shell Methods

Computing the Volume of a Solid of Revolution using the TiNspire CX CAS can easily be done – step by step – using the Calculus Made Easy at www.TinspireApps.com .

Here is how.

Let’s start with the Disk Method. We just select that option in the menu:

Then this pops up :

Now, enter the given function in the top box and the given interval below. Automatically, the answer will show in the bottom with correct integral setup and the correct answer.

Similarly, when using the Washer Method for two functions we have:

Finally, the Shell method works the same way :

In conclusion, the just like all other Calculus topics finding the Volume of Solids of Revolution using the Disk , Washer and Shell Methods can be done easily using Calculus Made Easy at www.TiNspireApps.com .

TiNspire Users in Finnland comments

Kuulin koulussa 3 ihmisen ryhmän puhuvan Calculus kurssista miten hän läpäisi kurssinsa sovelluksen, avulla joka näytti kaikki välivaihe ratkaisut.
Luokkakaveri oli puhunut myöskin ohjelmasta, jonka nimi oli Calculus made easy, mikä näytti kuulemma välivaihe ratkaisut.

Yhden matikan kurssin reputtaneena ja toisenkin ehkä myöskin, turhautumiseni matematiikka kolmannen matikan Calculus kurssiin alkoi olemaan stressaavaa.
Päätin ostaa Calculus Made easy ohjelma TI-Nspire CX CAS laskimeen, tämä ohjelman avulla olen onnistunut tekemään kotitehtäviä jotka, ovat olleet haastavia minulle! 
Erittäin hyödyllinen ohjelma niille jotka eivät ole keskiverto tasoa matikan laskemisessa.

Ti-Nspire : Step by Step Definite Integrals

Computing definite Integrals using the 1. Fundamental Theorem of Calculus can be achieved using Calculus Made Easy at https://www.tinspireapps.com/?a=CME

Use option 8 in the INTEGRATION menu

Enter function f(x) and bounds [a,b] as shown below

View the Integration steps, here, the Power Rule is applied.

Lastly, plug the bounds into the above Antiderivative, subtract and that’s it!

Ti NSpire CX: Implicit Differentiation – Step by Step

Using Calculus Made Easy on the TiNSpire CX at  https://www.tinspireapps.com/?a=CME

choose IMPLICIT DIFFERENTIATION in the menu , then enter  the equation of a

given curve as shown below:

The Implicit Differentiation process continues until step 5)

VOILA ! easy as pie! The handy TiNspire CX can not only Implicit Differentiation Step by Step but can do ALL

of Calculus Step by Step!

 

▷[Solved] Compute Limits in Calculus – Step by Step – using the TiNspire CX CAS

In your Calculus class you will be asked to compute limits. You should know that there is a variety of techniques to figure out limits such as via Factoring, via Common Denominator and of course via L’Hopital rule (which we covered in earlier posts already) . All these techniques can be applied using the Calculus Made Easy app , just navigate to Limits in the Menu as seen below:

When selecting the menu option 4: Limit via Factoring you enter your function and the x value that you are approaching. Now lean back and observe the steps to arrive at the limit. Calculus all of a sudden got easy! See below.

 

Another common method to compute Limits is via Common Denominator of the numerator. Read the sentence again to digest it better 😉

The tricky part is to enter the two fractions in the numerator properly, extra set of parentheses are needed here. See below

 

The steps to compute the limits are displayed below:

These Step by Step Limit computation methods using your TiNspire CX CAS will allow you to master your Calculus class.

▷Solved: Volume of Solid of Rotation by Washer Method using the TiNspire CX

Computing the Volume of a solid of rotation using the Washer or Shell Method

can easily be performed using TiNSpire’s Calculus Made Easy app as follows.

After selecting the Washer Method about x-axis just enter the upper U and lower function L

(dont worry in case you swap them : the answer will be correct except it will have a minus sign with it. )

and the interval bounds a and b as shown in belows image:

 

You can see the general washer method formula and how it is applied to you specific problem.

Additionally, you will see the antiderivative (if it is exists), the exact and finally the correct decimal answer.

Finding the volume of solids of rotation and with known cross sections are just a few integral applications included in the Calculus Made Easy app of your TiNspire. Other included applications are surface area of solids, curve lengths, center of math, improper integrals, etc

Best of all Calculus Made Easy can be used for 3 courses of Calculus: Calculus I, II and III, the latter being a typical Multivariable Calculus course which involves partial derivatives and multiple integrals.

 

 

▷Riemann Sums – Step by Step – with the TiNSpire CX CAS: Calculus Made Easy

Say you need to compute Riemann Sums at selected points over a given interval. And you do have your trusty TiNspire CX on you. Then start Calculus Made Easy , go to option 1 J in the menu and enter

  1. the given function
  2. the given interval
  3. the selected x-values c1, c2, ..

as shown in image

 

Then each Riemann rectangle is computed step by step as shown below :

Lastly, view the final Riemann Sum and compare it to the exact definite integral. Pretty close 😉

▷Integration by Parts – Step by Step – using the Tinspire CX : Calculus Made Easy

Integration by Parts with steps is easily done using Calculus Made Easy (download : www.tinspireapps.com ) under the Integration tab.

Enter your function as f(x) and your choices of u and v’ below.

See example in image:

Answer appears automatically with steps involved.

Steps for Integration and Differentiation and all other Calculus topics are included in the Calculus Made Easy app.

▷Relative Rate of Change using the TiNspire CX CAS

To find the Relative Rate of Change using the TiNSpire CX CAS open up Calculus Made Easy from www.TiNspireCX.com , then go menu item “Derivatives” and select “Relative Rate of Change”. Enter the given Function and Voila, the Relative Rate of Change shows immediately, Very simple to use !!!

 

Remember that Relative Rate of Change in Calculus is the Derivative of a Function divided by the Function itself. Here is an example:

f(x) = 4x + exp(7x) , then f'(x) = 4 + 7*exp(7x) ,

Thus , Relative Rate of Change of f =

(4 + 7*exp(7x) ) / (4x + exp(7x) )