SOLVED:Using the Trapezoidal Rule and Simpson's Rule In Exercises 3-14, use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n . Round your answer to four decimal places and compare the results with the exact value of the definite integral. ∫0^2 x e^-x d x, n=4
SOLVED:Using the Trapezoidal Rule and Simpson's Rule In Exercises 3-14, use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n . Round your answer to four decimal places and compare the results with the exact value of the definite integral. ∫0^2 x e^-x d x, n=4
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(a) Use the composite trapezoidal rule and the composite simpson's rule, separately, to approximate the integral ∫0^1 (dx)/(x 2) with n = 4. (b) Use the error formulas below to determine the values of n and h to approximate ∫0^1 (dx)/(x 2) to within 10^-6 by using 1) The composite trapezoid rule and 2) The composite simpsons rule. Composite Trapezoid Rule Error= -(1)/(12) f”(ξ)(b - a)h^2, ξ∈ (a, b) Composite Simpson's Rule Error= -(h^4(b - a))/(180) f^(4)(ξ), ξ∈ (a, b)
(a) Use the composite trapezoidal rule and the composite simpson's rule, separately, to approximate the integral ∫0^1 (dx)/(x 2) with n = 4. (b) Use the error formulas below to determine the values of n and h to approximate ∫0^1 (dx)/(x 2) to within 10^-6 by using 1) The composite trapezoid rule and 2) The composite simpsons rule. Composite Trapezoid Rule Error= -(1)/(12) f”(ξ)(b - a)h^2, ξ∈ (a, b) Composite Simpson's Rule Error= -(h^4(b - a))/(180) f^(4)(ξ), ξ∈ (a, b)
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