2. Numerical Methods

Numerical Integration — Quiz

Test your understanding of numerical integration with 5 practice questions.

Practice Questions

Question 1

What is the order of the global error for the composite Simpson’s rule as the subinterval width $h$ decreases?

Question 2

What are the standard node locations for the two-point Gauss–Legendre quadrature rule on the interval $[-1,1]$?

Question 3

Which change of variables transforms $\int_{a}^{b}f(x)\,dx$ into the standard form $\int_{-1}^{1}f\bigl(\tfrac{b-a}{2}t+\tfrac{a+b}{2}\bigr)\,dt\,$?

Question 4

To remove the algebraic singularity at $x=0$ in the integral $\int_{0}^{1}\frac{g(x)}{\sqrt{x}}\,dx\,$ which substitution is most appropriate?

Question 5

When using the composite trapezoidal rule with $n=2$ subintervals to approximate $\int_{0}^{1}e^{x}\,dx\,$, what is the approximate numerical value?