Calculus

Numerical Approximation of Integrals

Integral Approximation - Simpson's Rule

         

Using Simpson's rule, approximate ∫01(5x2+1)dx.\displaystyle{\int_0^1(5x^2+1)dx}.

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What is the error when approximating ∫06(6x2+2x−3)dx\displaystyle{\int_0^{6}(6x^2+2x-3)dx} using Simpson's rule?

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Approximate ∫06(x3−x2−7x−11)dx\displaystyle{\int_{0}^{6}(x^3-x^2-7x-11)dx} using Simpson's rule.

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Sam and Lisa are approximating the definite integral ∫04(3x2+2x+1)dx.\displaystyle{\int_0^{4}(3x^2+2x+1)dx}. Sam used the right Riemann sum with 44 intervals, and Lisa used Simpson's rule. If Sam's approximation is SS and Lisa's approximation is L,L, what is S−L?S-L?

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Given only the following three values of the function ff: f(0)=18,f(50)=14,f(100)=−5,f(0)=18, f(50)=14, f(100)=-5, approximate the integral ∫0100f(x)dx\displaystyle{\int_0^{100}f(x)dx} using Simpson's rule.

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