Suppose \(T, L,\) and \(R\) are the approximation values using the Trapezium rule, left Riemann sum, and right Riemann sum, respectively, of the integral \(\displaystyle{\int_0^{1}(16-x^2)dx}\) using \(19\) intervals. Which of the following is the correct relationship between the three approximations?

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Suppose \(T, L,\) and \(R\) are the approximation values using the Trapezium rule, left Riemann sum, and right Riemann sum, respectively, of the integral \(\displaystyle{\int_0^{17}(2x^3+3)dx}\) using \(15\) intervals. Which of the following is the correct relationship between the three approximation values?

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Which method gives the closest approximate value to the integral \(\displaystyle{\int_0^{4}4x^2 dx},\) a right Riemann sum, a left Riemann sum, or the Trapezium rule, where the same number of intervals is used for each approximation?

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Suppose the integral \(\displaystyle{\int_0^{3}3x^{3}dx}\) is approximated using a right Riemann sum and a left Riemann sum. Which sum gives a more accurate approximation to the integral?

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Sarah is approximating the integral \(\displaystyle{\int_0^{3}(4x+2)dx}\) using a Riemann sum. Would a right Riemann sum or left Riemann sum give a more accurate approximation?

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