Question

Calculus Help Please I know how to do Number 3 I just need help with detailed explaination of 1 and 2

Answer 1

(1) Using a trapezoidal sum, we approximate the integral by

$\displaystyle\int_0^8R(t)\,\mathrm dt\approx\frac{(R(0)+R(2))(2-0)+(R(3)+R(2))(3-2)+(R(7)+R(3))(7-3)+(R(8)+R(7))(8-7)}2$

$\displaystyle\int_0^8R(t)\,\mathrm dt\approx24.830$

measured in gallons of water.

(2) Notice that the table shows the specific values of $R(t)$ increasing, meaning $R'(t)>0$. There's not enough evidence to suggest that we have $R'(t)=0$ at any time.