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integration

1.double gauss_ch1(double(*f)(double),int n); 1−1f (x )dx √1−x 2

. n Gauss-Chebyeshev ; . [−1,1] 1√1−x 2

T n (x )=cos(n arccos(x )).T n (x ) [−1,1] n x k =cos(2k −12n π),k =1,···,n .n Gauss-Chebyeshev

1−1f (x )dx √1−x 2

≈πn n k =1f cos 2k −12n π 2.double gauss_ch2(double(*f)(double),int n); 1−1√

1−x 2f (x )dx .

n Gauss-Chebyeshev II ; . [−1,1] √1−x 2 U n (x )=sin((n +1)arccos(x )).U n (x ) [−1,1] n x k =cos(kπ),k =1,···,n .n Gauss-Chebyeshev II

1−1√

1−x 2f (x )dx ≈πn +1n k =1sin 2 kπn +1 f cos kπn +1

3.double comp_trep(double (*f)(double),double a,double b); b a f (x )dx .

; .

4.double romberg(double (*f)(double),double a,double b); b a f (x )dx .

Romberg ; .

1

integration

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