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# Use technology to approximate the given integrals with Riemann sums, using (a) n=10, (b) n=100, and (c) n=1,000. Round all answers to four decimal places. $\int_{2}^{3} \frac{2 x^{1.2}}{1+3.5 x^{4.7}} d x$

Solution

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Answered 1 month ago
Answered 1 month ago
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We will be using Octave , a free software similar to Matlab.
a.
The code that computes the left Riemann sum is

    n = 10;
a = 2;
b = 3;

dx = (b-a)/n;

grid = a:dx:b-dx;
left_r_sum = 0;

for i = 0:n-1
left_r_sum = left_r_sum+(2*grid(i+1)^(1.2))/(1+3.5*grid(i+1)^(4.7));
endfor

left_r_sum = left_r_sum*dx



The result is

$\int_2^3 \dfrac{2x^{1.2}}{1+3.5x^{4.7}}\dd{x} \approx 0.0275$

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