Holistic Numerical Methods Institute
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Multiple Choice Test
Gauss Quadrature Rule of Integration
Q1.
is exactly
Q2. For a definite integral of any third order polynomial, the two-point Gauss quadrature rule will give the same results as the
1-segment trapezoidal rule
2-segment trapezoidal rule
3-segment trapezoidal rule
Simpson's 1/3 rule
Q3. The value of
by using the two-point Gauss quadrature rule is most nearly
11.672
11.807
12.811
14.633
Q4. A scientist uses the one-point Gauss quadrature rule based on getting exact results of integration for functions f(x)=1 and x. The one-point Gauss quadrature rule approximation for
Q5. A scientist develops an approximate formula for integration as
where
The values of c1 and x1 are found by assuming that the formula is exact for the functions of the form a0x + a1x2 polynomial. Then the resulting formula would therefore be exact for integrating
Q6. You are asked to estimate the water flow rate in a pipe of radius 2m at a remote area location with a harsh environment. You already know that velocity varies along the radial location, but you do not know how it varies. The flow rate Q is given by
To save money, you are allowed to put only two velocity probes (these probes send the data to the central office in New York, NY via satellite) in the pipe. Radial location, r is measured from the center of the pipe, that is r=0 is the center of the pipe and r=2m is the pipe radius. The radial locations you would suggest for the two velocity probes for the most accurate calculation of the flow rate are
0,2
1,2
0,1
0.42,1.58
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