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score on last try: 0 of 5 pts. see details for more. get a similar question you can retry this question below the following table shows the rate of water flow (in l/min) through a dam. t (min) 1 6 11 16 21 26 31 v(t) (l/min) 10 10 10 8 2 9 1 approximate the total volume of water that passed through the dam from t=1 to t=31 using simpsons rule, with n=6. 235 x liters question help: video

score on last try: 0 of 5 pts. see details for more. get a similar question you can retry this question below the following table shows the rate of water flow (in l/min) through a dam. t (min) 1 6 11 16 21 26 31 v(t) (l/min) 10 10 10 8 2 9 1 approximate the total volume of water that passed through the dam from t=1 to t=31 using simpsons rule, with n=6. 235 x liters question help: video

Answer

Explanation:

Step1: Identify the interval and step - size

The interval is $[a = 1,b = 31]$ and $n = 6$. The step - size $\Delta t=\frac{b - a}{n}=\frac{31 - 1}{6}=5$.

Step2: Recall Simpson's rule formula

The formula for Simpson's rule to approximate $\int_{a}^{b}V'(t)dt$ is $S_n=\frac{\Delta t}{3}[V'(t_0)+4V'(t_1)+2V'(t_2)+4V'(t_3)+2V'(t_4)+4V'(t_5)+V'(t_6)]$, where $t_i=a + i\Delta t$ for $i = 0,1,\cdots,6$.

Step3: Substitute the values

$t_0 = 1,t_1 = 6,t_2 = 11,t_3 = 16,t_4 = 21,t_5 = 26,t_6 = 31$; $V'(t_0)=10,V'(t_1)=10,V'(t_2)=10,V'(t_3)=8,V'(t_4)=2,V'(t_5)=9,V'(t_6)=1$. $S_6=\frac{5}{3}[10 + 4\times10+2\times10+4\times8+2\times2+4\times9+1]$ $=\frac{5}{3}[10 + 40+20+32+4+36+1]$ $=\frac{5}{3}(143)$ $=\frac{715}{3}\approx238.33$.

Answer:

$\frac{715}{3}\approx238.33$ liters