Given that f(x) = x -0.3x -8.56x+8.448. (35%) -2 a. Approximate f f(x) dx with 20...

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Given that f(x) = x³ -0.3x² -8.56x+8.448. (35%) -2π a. Approximate f f(x) dx with 20 evenly-spaced grid points over the whole interval using Riemann Integral, Trapezoid Rule, and Simpson's Rule. Explain the difference behind each of the method. b. Compared to the methods above, do you think that explicit integration could be more convenient to be done? c. Use polynomial interpolation to compute f'(x) and f"(x) at x = 0, using the discrete data below -1.1 -0.3 0.8 1.9 15.180 10.962 1.920 -2.040 x f(x) d. Calculate the accuracy result compared to the initial f (x) Given that f(x) = x³ -0.3x² -8.56x+8.448. (35%) -2π a. Approximate f f(x) dx with 20 evenly-spaced grid points over the whole interval using Riemann Integral, Trapezoid Rule, and Simpson's Rule. Explain the difference behind each of the method. b. Compared to the methods above, do you think that explicit integration could be more convenient to be done? c. Use polynomial interpolation to compute f'(x) and f"(x) at x = 0, using the discrete data below -1.1 -0.3 0.8 1.9 15.180 10.962 1.920 -2.040 x f(x) d. Calculate the accuracy result compared to the initial f (x) Given that f(x) = x³ -0.3x² -8.56x+8.448. (35%) -2π a. Approximate f f(x) dx with 20 evenly-spaced grid points over the whole interval using Riemann Integral, Trapezoid Rule, and Simpson's Rule. Explain the difference behind each of the method. b. Compared to the methods above, do you think that explicit integration could be more convenient to be done? c. Use polynomial interpolation to compute f'(x) and f"(x) at x = 0, using the discrete data below -1.1 -0.3 0.8 1.9 15.180 10.962 1.920 -2.040 x f(x) d. Calculate the accuracy result compared to the initial f (x) Given that f(x) = x³ -0.3x² -8.56x+8.448. (35%) -2π a. Approximate f f(x) dx with 20 evenly-spaced grid points over the whole interval using Riemann Integral, Trapezoid Rule, and Simpson's Rule. Explain the difference behind each of the method. b. Compared to the methods above, do you think that explicit integration could be more convenient to be done? c. Use polynomial interpolation to compute f'(x) and f"(x) at x = 0, using the discrete data below -1.1 -0.3 0.8 1.9 15.180 10.962 1.920 -2.040 x f(x) d. Calculate the accuracy result compared to the initial f (x)