Definite integrals using calculator

[Cream Soda]

I'm doing some math homeowork atm and I'm not sure what I'm doing wrong input-wise to get the incorrect answer. On these particular problems, I am working them by hand and getting them correct, but there will be problems where we are asked to use the calculator to integrate and if I'm coming up with the incorrect answers now, I sure will later as well.

For example, we have
2 * Integral from 0 to 2 (4x - ((x^3)/3)

That gives me

2*[(4*2 )- ((2^3)/3)] - [(4x0)-((0^3))/3)]
2*[(8 )-(8/3)] -0= 16/3
2*(16/3) =
32/3, which is what i get from the back of the book

But when I go to Integrate it on my TI-84, it keeps giving me a different answer

math 9 gives me fnInt(
So i do
2*fnINT((4x)-((x^3)/3),x,0,2
and it gives me 40/3

[Tokitoki]

If its an Integral of 2*[4x-((x^3)/3)] from 0 to 2 then it should look like this:

=> 2*[2x^2 - ((x^4)/12)] 0 to 2
= 2*[2*2^2-((2^4)/12)]
=2*[24/3-4/3]
=2*[20/3]
= 40/3

You never acutally integrated the eqn when you did it by hand is what it looks like to me.

[Cream Soda]

Oops, i see where i screwed up. I used the calculator to take the integral of what I already took the integral of by hand, not the original integral. /facepalm

[Tokitoki]

The original eqn was 4-(x^2) then?

[Cream Soda]

Correct. Thanks for the help lol going over what you said made me go oh wtf that wasn't the original equation. I was just trying to sum them up I think