Question

PLS HELP CALCULUS MORE COMING PLS PLS PLS I NEED TO PASS

Answer 1

$\displaystyle\int_0^5R(t)\,\mathrm dt\approx\sum_{i=1}^4\frac{R(t_i)+R(t_{i-1})}2\Delta t_i$

where $t_0=0,t_1=1,t_2=2,t_3=4,t_4=5$, and we define $\Delta t_i=t_i-t_{i-1}$ for $i\ge1$. The sum is adding up the areas of several trapezoids, each with dimensions determined by the values of $t_i$ and $R(t_i)$. (See the picture below)

So the number of deliveries made is approximately

$\displaystyle\frac{(250+100)(1-0)+(200+250)(2-1)+(350+200)(4-2)+(100+350)(5-4)}2=1175$