Calculus
Numerical Approximation of Integrals
Using Simpson's rule, approximate \(\displaystyle{\int_0^1(5x^2+1)dx}.\)
What is the error when approximating \(\displaystyle{\int_0^{6}(6x^2+2x-3)dx}\) using Simpson's rule?
Approximate \(\displaystyle{\int_{0}^{6}(x^3-x^2-7x-11)dx}\) using Simpson's rule.
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 \(S-L?\)
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.