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If you want to find a triple integral using the TI nSpire it's very straightforward. It's exactly the
same as finding a regular integral. First go to Menu, then go to Calculus
go to integral.
If I'm going to do a triple integral I will put the outside bounds in first for the integral that I'm looking at, I will put in -2 to 2
That's the first integral. Here in this box, go to Menu, Calculus, Integral again put in your second set of bounds
I've got a complicated one here. Negative square root 8 - x squared,
to the positive square root
8 - x squared
In this box I'm going to put another integral. So go to calculus
integrate. I can put my inner bounds which in my case was x squared
plus z squared
up here I can put my other bound which is 16 - 3 x squared.
- z squared
and then I put in here. In my case I'm just trying to find a volume so I'm doing dy
times dz times dx. So I do want to put a 1 there, because there's nothing, there's no function.
so i put dy
dz, dx
I hit enter. That calculates it pretty straightforward. Uh, I actually did mine wrong for my class watching this. I'm going to do it
one more time.
so go back up here
copy this and bring it back down here. I actually wanted to put 2 here.
There we go. So our answer was 32 pi square roots of 2. I'm going to do one more.
I'm going to go to menu, another way you could do this is hit integral,
click menu calculus
and then menu calculus, integral. So my inner function for this specific one that I'm doing is 0 to x
the next one is 0 to z
and the next one is 0 to 4 root pi. The fourth root of pi, sorry. And the fourth root is here. I type that to get fourth root.
of pi
and my function was 12, and you do need to put a times here, i'm not sure why but sometimes it prefers it. 12 times y squared, times z cubed
times
at times the sine of x to the fourth. You can see why I don't want to integrate this bad boy.
And that is with respec to dy
dx and dz.
hit enter, and I get pi over 4. So all that to get pi over 4. It's pretty amazing that your calculator can do triple integrals like that
I would definitely do ones by hand that are more straightforward, but ones with functions within functions can definitely be more challenging.
Make sure you can do them by hand and check yourself using the calculator. If you have any questions about that please let me know.