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 MULTIPLE CHOICE TEST GAUSS QUADRATURE RULE INTEGRATION

Pick the most appropriate answer

 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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