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# Lab 9 - ECOR 1606 Practice Lab Final The Sine Integral is...

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ECOR 1606 Practice Lab Final The Sine Integral is defined as ( ) ( ) = x dt t t x Si 0 sin Gauss-Legendre quadrature can be used to accurately approximate Si ( x ). The approximation is: ( ) = 4 0 sin ) ( n n n x A x Si τ where A 0 = 2.5253303767 τ 0 = 0.0469100770 A 1 = 1.0370462484 τ 1 = 0.2307653450 A 2 = 0.5688888889 τ 2 = 0.5000000000 A 3 = 0.3111070642 τ 3 = 0.7692346550 A 4 = 0.1242940878 τ 4 = 0.9530899230 examples: Si (1) = 0.946083 Si (2) = 1.60541 Si (3) = 1.84865 Write a C++ function that, given x , approximates Si ( x ) and returns the result. Note that it is NOT necessary to convert from degrees from radians when using function sin because the argument is already in radians. Then write a C++ program that finds the largest and smallest values of Si ( x ) for b x a . The largest and smallest values are to be found by evaluating Si ( x ) at N equally spaced values for x , starting with x = a and ending with x = b . Your program must make use of the function required above. Your program should repeatedly read in values for a , b , and N until 0 0 0 is entered. Note that N is an integer. For each set of values entered your program should either i) output an error message (if the

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