Question

The rate of oil imports to the U.S. from Mexico can be approximated by r(t)=5.48t2+36.5t+510r(t)=-5.48 t^{2}+36.5 t+510 million barrels per year (0t8)(0 \leq t \leq 8) where t is time in years since the start of 2000. Estimate 08r(t)dt\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

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Answered 4 months ago
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We'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][0,8] with n=150n = 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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