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Language: Numerical Integration
Description In his freshman year, flymouse studied integral. Symbolic integration frustrated him a lot. He was often confused by those subtle techniques: alternately trying integration by substitution and integration by parts until the integrand appears in a tabulated form then employing integration by quadrature to have the work finally done. In contrast, numerical integration intrigued him much. By following some fixed procedures such as Newton-Cotes formulas, he could easily find the approximation to some definite integrals without too much effort. Given the exercises flymouse did, can your program do as nice a job as flymouse did? Input The input contains several test cases. Each test case consists of one line containing a univariate function
And the syntax is given below:
Operator precedence and associativity are almost the same as those in C except that ‘
Length of the interval over which Process to end of file. Output For each test case, output one line with only the approximate value of the integral rounded to exactly four digits past the decimal point. Sample Input x+1 0 1 +x 0 1 x-1 0 1 -x 0 1 x*x 0 1 x/2 0 1 x^-x 0 1 (x+1)*x 0 1 -(x+1) 0 1 sin(x) 0 1 cos(x) 0 1 tan(x) 0 1 log(x) 1 2 exp(x) 0 1 asin(x) 0 1 acos(x) 0 1 atan(x) 0 1 abs(x) 0 1 x 0 1 1 0 1 sin(x)/x 0 1 Sample Output 1.5000 0.5000 -0.5000 -0.5000 0.3333 0.2500 1.2913 0.8333 -1.5000 0.4597 0.8415 0.6156 0.3863 1.7183 0.5708 1.0000 0.4388 0.5000 0.5000 1.0000 0.9461 Hint - Be cautious about outputting ‘
`-0.0000` ’. - Make your integration module as robust as possible.
Source POJ Monthly--2006.12.31, galaxy |

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