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Question

The rate of oil imports to the U.S. from Mexico can be approximated by $r(t)=-5.48 t^{2}+36.5 t+510$ million barrels per year $(0 \leq t \leq 8)$ where t is time in years since the start of 2000. Estimate $\int_{0}^{8} r(t) d t$ using a Riemann sum with n=150. (Round your answer to three significant digits.) Interpret the answer.

Solution

VerifiedAnswered 4 months ago

Answered 4 months ago

Step 1

1 of 3We'll be using Octave, a free software similar to Matlab. Here is the code that computes the left Riemann sum on the interval $[0,8]$ with $n = 150$ subdivisions.

```
n = 150;
a = 0;
b = 8;
dx = (b-a)/n;
grid = a:dx:b-dx;
left_r_sum = 0;
for i = 0:n-1
t = grid(i+1);
pt = -5.48*t^2+36.5*t+510;
left_r_sum = left_r_sum+pt;
endfor
left_r_sum = left_r_sum*dx
```

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