Question

I need some help with this calculus assignment Second part is How much is spent on the job from the 12th to the 20th day

Answer 1

rate of change = f(x) = 4.1x + 1.9

Since we want the total expenditure if the job takes 12 days, we must integrate the expression above from 0 to 12. Like this:

$\text{Total expenditure=}\int f(x)dx\text{ from x = 0 to x = 12}$$\begin{gathered} \int ^{^{12}_{}}_04.1x+1.9dx \\ =\frac{4.1x^2}{2}+1.9x\rbrack^{12}_0= \\ =\frac{4.1}{2}(12^2-0^2_{})+1.9(12-0)= \\ =4.1\times72+1.9\times12= \\ =295.2+22.8= \\ =318 \end{gathered}$

So our final answer is:

$\text{Total expenditure=318}$