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integration

integration
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 ?1

2n π),k =1,···,n .n Gauss-Chebyeshev

1

?1

f (x )dx √1?x 2

πn n k =1f cos 2k ?1

2n 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 =1

sin 2

kπn +1

f cos

n +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

5.double gauss_leg_9(double(*f)); 1

?1

f(x)dx.

9 Gauss-Legendre .

? :

1?1e x

1?x2dx

=

1

?1

xe x

1?x2

dx

1

2

3

4

5

? 3,4,5 :

π

2

sin xdx(=1)

3

4

5

2

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