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Module 5 Problems1.Evaluate the Riemann sum for (x) = x3− 6x, for 0 ≤ x≤ 3 with six subintervals, taking the sample points, xi, to be the right endpoint of each interval. Give three decimal places in your answer. 2.Explain, using a graph of f(x), what the Riemann sum in Question #1 represents
3.Express the given integral as the limit of a Riemann sum but do not evaluate:
3i3−6(3i)n∗3n¿¿∑i=n¿limn→ ∞¿4.Use the Fundamental Theorem to evaluate (Your answer must include the antiderivative.) .∫3x3−6xX^4/4 – 3x^2 + C3^4/4 – 3(3)^2 = 20.25-27=-6.750^4/4 – 3(0)^2 = 0 – 0=0-6.75-0=6.75(0.5)3.3755.Use a graph of the function to explain the geometric meaning of the value of the integral.
The approximate area under of the graph x^3-6x with six subinterval on an interval of [0, 3] is 3.375.