Master the Net Change Theorem with Expert Homework Statement Help

[Slimsta]

Homework Statement

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Homework Equations

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?

 

[Mark44]

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.

 

[Slimsta]

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

so how do i express the antiderivative?

 

[Mark44]

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

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

 

[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!