Please check my work :) Evaluating integrals

Question

babynini · Answer

$$\int\limits_{0}^{3}2\left| x^2-4 \right|dx$$

babynini · Answer

In the end I got = 19
If that's incorrect I could write out my entire process :)

aravindg · Answer

You need to evaluate this in intervals.

babynini · Answer

$$\int\limits_{0}^{2}2(4-x^2)+\int\limits_{2}^{3}2(x^2-4)$$ this is how I did it :) is that correct?

aravindg · Answer

Well done!

babynini · Answer

And the answer does come out to 19?

aravindg · Answer

Let me check that. You process is right.

dannyo19 · Answer

I don't think it's 19

babynini · Answer

hmm
$$8x-(2x^3)/3 $$ evaluated at a=0, b=2
$$(2x^3)/3-8x$$ evaluated at a=2, b = 3

babynini · Answer

= 8+(3-(-8)) = 19

aravindg · Answer

For case 1

8*2-2*2^3/3
16-16/3
16(1-1/3)
16(2/3)
32/3

babynini · Answer

oh woah I think I went off on the 2*x^3 part. woops.

babynini · Answer

46/3  is it?

dannyo19 · Answer

Yes

aravindg · Answer

Now it is done ;)

babynini · Answer

Yay!! thank you so much :)
I think I had dropped the 2 on accident o.o

babynini · Answer

Yall are life savers heh

aravindg · Answer

Accidents doe >.>

babynini · Answer

Ikr :| the ones that change your grade by a whole letter hahah

aravindg · Answer

:| Exactly

babynini · Answer

smh. Well thanks again:) I only have one left kekek. I will probably post it in a new question soon.