ЗАДАНИЯ

Вычислить интеграл от функции F (x) на отрезке [a,b] с точностью ε = 0,001 методом трапеций и Симпсона. Сравнить полученные результаты.

1. F (x)=

ex −1 , a = 0.2,

b = 2.1.

2.

F (x)= ex sin x,

a = 0.0,

b =π 2.

3. F (x)=

(

x2

)

10−2 x , a =1.0,

b = 0.5.

−1

4.

F (x)= x 3 1 + x,

a =1.0,

b =8.0.

5. F (x)=

1

a = 0.0,

b =π 2.

3 + 2cos x ,

6. F (x)=

1

,

a = 2.0,

b = 2.7.

x ln2

x

7.

F (x)= arcsin

x

,

a = 0.2,

b = 0.3.

x(1 − x)

8.

F (x)= x3e2 x ,

a = 0.0,

b = 0.8.

9.

F (x)=tg

3

x

+

π

,

a = 0.0,

b =π 8.

2

4

10. F (x)= x arctg x,

a = 0.0,

b =1.7.

11. F (x)=

1

,

a = 0.0,

b = 2.0.

1 +

x

12. F (x)=

1

,

a = 0.0,

b =

3

.

5 −3cos x

2π

13. F (x)=

2

,

a = −2.0,

b = −1.2.

1 −4x

14. F (x)=

1

,

a = 0.0,

b = 0.6.

(x +1)

x2 +1

15. F (x)=

2

,

a = −2.0,

b = −1.2.

1 −4x

16. F (x)=

x

,

a =1,

b =5.

(1 + 2x)2

17. F (x)=

1

,

a = −2,

b = 2.

3x2 + 4x + 2

15

18. F (x)=		x			,	a = −1,			b =1.
	(3x + 4)3
19. F (x)= x3		4 + x2 ,					a =1, b =5.
20. F (x)= ex		,	a = 0.1,				b =1.
	x
21. F (x)= esin x ,			a = 0,				b = 0.5.
22. F (x)=	cos x,				a = 0,			b =	π .
									6
23. F (x)=		1		,		a = 0.0,			b = 0.5.
	x4 +1
24. F (x)= sin x			,	a = 0.0,				b = π .
	x								3
25. F (x)= arctg				x −1,				a =1, b =16.

16