Numerical Integration review

Two applications where numerical integration is used are integrating discrete data points and when it is difficult or impossible to obtain an analytic solution.

• True

• False

If the error of an integration technique is proportional to h², we say the error is of order h², which we write as O(1/h²).

• True

• False

The Trapezoidal rule approximates the function by a _____ order polynomial

• 1st

• 2nd

• 3rd

• none of these

The only way to increase the accuracy using Newton-Cotes integration techniques is to increase the order of the approximating polynomial

• True

• False

A single application of the Simpson's 1/3 rule requires computing the value of the function at ___ points

• 2

• 3

• 4

• 1

Simpson's 3/8 rule approximates the function with a ___-order polynomial

• first

• second

• third

• none of these

Choose the integration technique that MUST be used for unequal-width segments

• trapezoidal

• hybrid Simpson's

• Gauss-Legendre

• Simpson's 1/3

How many points would we need to approximate a double integral using a single application of Simpson's 1/3

• 4

• 9

• 16

• 25

Gauss Quadrature is a class of techniques for evaluating the area under a straight line by joining function values at any two points rather than just the end points.

• True

• False

The point of Gauss Quadrature is to balance the function values

• True

• False