For the following problems, the units $of$ a variable are given

along with the units for a function $(or$ two functions$).$ Give the

units $of$ each definite integral.

$(a)Ifxisin$ "seconds" and $f(x)isin$ "fee$\frac{t}{second"\text{t}\text{h}\text{e}\text{n}}{\displaystyle \underset{a}{\overset{b}{}}}f(x)dx$

$isin$

$\left[\begin{array}{c}\text{f}\text{e}\text{e}\text{t}\frac{?}{se{c}^2}\\ \text{f}\text{e}\text{e}\text{t}\frac{?}{sec}\\ \text{f}\text{e}\text{e}\text{t}\\ \text{f}\text{e}\text{e}\text{t}*sec\end{array}\right]$

$(b)Iftisin$ "seconds" and $g(t)isin$ "fee$\frac{t}{(seconds{)}^{2n}}$ then ${\displaystyle \underset{a}{\overset{b}{}}}g(t)dt$

$isin$

fee$\frac{t}{sec{?}^{(}()2)}$

$$

fee$\frac{t}{sec}$

feet

feet$*sec$

$,$

$(c)Ifxisin$ "days" and $f(x)isin$ "degrees $F"$ then ${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx$

$isin$

days

$\frac{\text{d}\text{e}\text{g}\text{r}\text{e}\text{e}\text{s}F}{d}ay$

degrees $F$

$(degreesF)-$days

$(d)Ifxisin$ "hours" and $g(x)isin$ "kilowatts" then ${\displaystyle \underset{a}{\overset{b}{}}}g(x)dx$

$isin$

kilowatts

hours

kilowatt$\frac{s}{h}$our

kilowatts$-$hours

$(e)IfLisin$ "meters" and $f(L)isin$ "square meters" then

${\displaystyle \underset{a}{\overset{b}{}}}f(L)dLisin$

meters ${?}^{(}3)$

meters ${?}^{(}2)$

meters

$\frac{1}{m}$eters

$(f)Iftisin$ "minutes," $g(t)isin$ "gallon$\frac{s}{f}$oot," and $v(t)isin$

"fee$\frac{t}{m}$inute," then ${\displaystyle \underset{a}{\overset{b}{}}}g(t)v(t)dt*$ minutess $isin$ "seconds" and $f(s)isin$ "fee$\frac{t}{second"\text{t}\text{h}\text{e}\text{n}}{\displaystyle \underset{a}{\overset{b}{}}}(f(s){)}^{2}ds$

$isin$

feet $\frac{{?}^2}{se{c}^2}$

feet $\frac{{?}^2}{sec}$

feet

feet $*sec$

$(h)Ifxisin$ "days" and $f(x)isin$ "pounds" then ${\displaystyle \underset{a}{\overset{b}{}}}\frac{1}{f(x)}dx$

$isin$

$\frac{1}{p}$ounds

pounds

day$\frac{s}{p}$ound

pounds days

$(i)Ifxisin$ "inches," $A(x)isin$ "square inches," and $d(x)isin$

"pounds per cubic inch," then ${\displaystyle \underset{a}{\overset{b}{}}}A(x)d(x)dxisin$

pound$\frac{s}{i}$nches ${?}^{(}3)$

pound$\frac{s}{i}$nches ${?}^{(}2)$

pound$\frac{s}{i}nch$

pounds