Question

Use the Treceroidal puie and Simpsen's Rule to appreximate the value of the definite integral for the given value of n. Round your ansmers to four decimal ploces and campore the results with the eact velue of the delhine integral.∫¹₀ x³dx∅=4 Trapezoldal simpron's exact

Answer 1

The integral ∫¹₀ x³ dx is approximated using the Trapezoidal Rule and Simpson's Rule for n = 4 intervals, then compared to the exact value.

Step-by-step explanation:

The question asks to approximate the value of the integral ∫¹₀ x³ dx using the Trapezoidal Rule and Simpson's Rule for n = 4 intervals, and compare the results with the exact value of the integral. To start, for the Trapezoidal Rule, you divide the interval [0,1] into n equal parts, calculate the values of the function at these points, and apply the trapezoidal formula. For Simpson's Rule, you also divide the interval into equal parts, but you use parabolas to approximate the area under the curve, and this usually provides a more accurate approximation than the Trapezoidal Rule. Calculations will be performed to obtain the numerical solutions and then compared with the exact solution.