Net Change Theorem help

1. Jan 16, 2010

Slimsta

1. The problem statement, all variables and given/known data
http://img39.imageshack.us/img39/8019/92452636.jpg [Broken]

2. Relevant equations

3. The attempt at a solution
i got -234 for the last part but it should be abs.value so 234.. but it didnt work.
is my work correct?

Last edited by a moderator: May 4, 2017
2. Jan 16, 2010

Staff: Mentor

No. You have v(t) = (t - 8)(t + 3), which is correct, but it's not true that v(t) <= 0 on the interval [6, 11]. Where did the 11 come from? Think about what the factors of v(t) mean. v(t) = 0 only for t = -3 and t = 8. These two numbers divide the number line into three regions, on two of which v(t) > 0 and on one of which v(t) < 0.

3. Jan 16, 2010

Slimsta

v(t) > 0 on [-infinity,-3] and [8, infinity]
v(t) < 0 on [-3, 8]

so how do i express the antiderivative?

4. Jan 16, 2010

Staff: Mentor

$$\int_6^{12} |v(t)|dt~=~\int_6^8 -v(t) dt~+~\int_8^{12} v(t) dt$$

Isn't that what you're trying to do?

5. Jan 16, 2010

Slimsta

that what i didnt understand how to set up..
so pretty much you take the number you got for t (which was t= -3, 8)
you pick the one that in the interval [6, 12] (in this case, 8)
and then make it 6 -- > 8 + 8 --> 12
i got it. sweet tnx a lot!