few will be a bit more subtle. For each question think carefully about the order in which you should be doing things since this can dramatically change the result.

Consider the vector vec$(v)=0\mathrm{.}5t^7$hat$()-12t^2$hat$().$ Using this vector, evaluate each of the following derivatives at $t=1\mathrm{.}8.$

Derivative

Magnitude of the derivative

$$

Derivative of the magnitude

$\frac{d|(vec(v))|}{dt}{|}_t||=1\mathrm{.}8=$

$$

Magnitude of the integral

Now consider the vector vec$(v)=4$that$()-6$that$()$ and evaluate the following definite integral.

$|{\displaystyle \underset{2}{\overset{2}{}}}(vec(v))dt|=$

Integral of the magnitude

Again consider the vector vec$(v)=4$that$()-6$that$()$ and evaluate the following definite integral.

${\displaystyle \underset{2}{\overset{2}{}}}|vec(v)|dt=$

$$