Numerical Approximation of Integrals

Concept Quizzes

Riemann Sums and Definite Integrals
Integral Approximation - Trapezium Rule
Integral Approximation - Simpson's Rule
Integral Approximation - Accuracy of Approaches
Integral Approximation - Increasing Intervals

Challenge Quizzes

Numerical Approximation of Integrals: Level 4 Challenges

Integral Approximation - Simpson's Rule

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

\frac{14}{3}

\frac{8}{3}

\frac{2}{3}

\frac{11}{3}

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by Brilliant Staff

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

2 5 8 0

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

60 51 57 54

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

-\frac{95}{7}

\frac{95}{7}

-30

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

2025 900 1150 1041

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by Brilliant Staff

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