Rozrakhunkovi_z_vischoyi_matematiki (1)

			46				X						-1				0	4
	.29
							p						0,2				0,7	0,1
				46			X						1				3	4
			.30
							p						0,1				0,8	0,1
			.
															0,			1,
															1 ,
											f x 1							1 x 5,
														8	0,			x 5.
														F x .
														X . f x ,					F x .
			.								f x .
													f(x)
											0,5
											0		1				5	x
															. 14.
:
											0,					1,
F		x		x	f		x dx	x	1		x	1	dx,			1 x 5,
									8
								1
								5	1	x 1 dx,
																5,
								1	8
															111

			0,		1,
		1
	F x		x 1 2 ,		1 x 5,
	16		1,		5.

F x :

F(x)

1

							0		1								5					x
												. 15.
						5	1							11
	M X x f x dx					x		x 1 dx								.
							8						3
						1
																														2
	D																	X			x2	f				M		X
																								x dx
	5	2		1				11				2	8
	, D(x) x				x 1 dx										.
				8					3				9
	1

47.

X F (x) .

f (x) , X

, . F (x) f (x) .

0, x 4

	47.1. F x (x 4)2 ,			4 x 5;	4, 2;	4,9.
			1, x 5
		0,		x 2
		1
	47.2. F x		(x 2)2 , 2 x 5;		3;	4.
		9
				x 5
		1,

112

								0,		x 0
	47.3. F x	1				x3 3x ,					0 x 2;					1; 1,5.
	2							1,		x 2
								0,		x 0
	47.4. F x		1				3x x2 ,				0 x 2;						0,5;		1.
	2							1,		x 2
								0,		x 0
	47.5. F x		1				4x2 x ,				0 x 1;						0,3;		0,5.
	3							1,		x 3
								0,		x 3
	47.6. F x x 3 2 , 3 x 4;														3,		3,5.
								1,	x 4
										x 1
								0,
	47.7. F x	1				x2 x 1 x 2;									1,		1,5.
	2							1,		x 2
						0,		x 0
	47.8. F x x3 ,							0 x 1;					0, 2,				0,5.
						1,		x 1
								0,		x 0
													1
	47.9. F x 3x2 2x, 0 x													;		0,1,		0, 25.
											1		3
								1,	x
											3
								0,		x 2
	47.10. F x			x			1,		2 x 4;							2,5,		3,5.
	2							1,	x 4

113

		0,			x 0
		1
	47.11. F x			x2 ,	0 x 3;					1, 1,5.
		9
					x 3
		1,
		0,			x 0
		1
	47.12. F x			x2 ,	0 x 2;					1, 1.
	4				x 2
		1,
		0,			x
								2
	47.13. F x cos x,						x 0;					, 0.
					2					3

1, x 0

		0,			x 0
	47.14. F x sin 2x,				0 x										;						;	.
									4										6
			1, x
							4
		0,			x				3
									4
						3															5
	47.15. F x cos 2x,								x ;														;	.
				1,	4														6
						x
				0,		x 1
																4									6
	47.16. F x (3x 3)2 , 1 x																;	0;								.
									3															5
				1,		x			4
									3
		0,		x 0
		1
	47.17. F x		x,	0 x 2; 1;															1, 2.
	2			x 2
		1,

114

					0,	x 1
			1
	47.18. F x			x2 1 , 1 x 2;													1,3;			1, 6.
			3
					1,	x 2
				0,	x 0
	47.19. F x sin x,				0 x								;			;	.
							2								6
				1,	x
							2
					0,		x 0
			1
	47.20. F x			x3 x , 0 x 2;											1;			1,3.
			6
					1,	x 2
				0,		x						1
							2
										1								1
	47.21. F x (2x 1)2 ,										x 0;								;	1.
							2											4

1, x 0

		0,		x 0
		x
	47.22. F x sin		,	0 x ;		; .
		2		4

1, x

2

0, x 1

		2
		1			2
	47.23. F x (2x 1)2 ,		x 1;			; 2.
		2		3

1, x 1

		0,		x 0
47.24. F x	x2		,	0 x 4; 1; 3.
16				x 1
		1,

115

									0,				x 2
							x			1																						1
	47.25. F x										,		2 x 2;																						;		0.
						4			2				x 2																	2
									1,
									0,					x 2
																											5												5
	47.26. F		x				2x		4					2 , 2 x															;	1;											.
																											2											4
																			5
									1,					x
																			2
									0,					x							2
																			3
																2															7
	47.27. F x 3x 2 2 ,																					x 1;												;				1.
									1,					3																9
														x 1
									0,					x								1
																			4
															1											1							1							4
	47.28. F x 4x 1 2 ,																	x										;								;						.
														4					1								2			3								10
									1,					x
																			2
									0,			x 1
	47.29. F x x3 1,											1 x 0;																		0,5;									0, 2.

1, x 0

0, x 2

47.30. F x (x 2)		2 ,	2 x 3;	2,3;	2,9.
	1,	x 3
			48.
			X			f (x) .
X .

x

F x f t dt . f (x) F (x) .

116

				0,	x 1
			1
	48.1.	f x		x 1 , 1 x 3 .
		2		0, x 2
					x 3
				0,
	48.2.	f x 0,5 x 3 , 3 x 5 .
				0,	x 5
				0,	x						1
					4
							1
	48.3.	f x 8 4x 1 ,								x 0 .
				0,	4
					x 0
				0,	x			4
					5
						4
	48.4.	f x 10 5x 4 ,							x 1.
				0,	5
					x 1
				0,	x 0
			1
	48.5.	f x		3x2 1 , 0 x 1.
			2
				0,	x 1

			0,	x						1
				5
48.6.	f x 4 2x 5 ,					5			x 3 .
			0,	2
				x 3
			0,	x					2
				3
48.7.	f x	6 3x 2 ,			2		x 1.
				3
			0,
				x 1

117

0, x 1

					0,	x 1
														4
	48.8.	f x	18 x 1 , 1 x														.
								3
					0,	x	4
							3
					0,	x 1
	48.9.	f x 2 x 1 , 1 x 2 .
					0, x 2
					0,	x 2
	48.10. f x			8 x 2 , 2 x												5		.
								2
					0,	x		5
								2
													1
					0, x
								2
	48.11. f x 4 2x 1 ,									1		x 0 .
								2
					0, x 0

0, x 0

48.12.f x 1 x, 0 x 2 .

2

0, x 2

0, x 0

48.13.f x 2x, 0 x 1.

0, x 3

48.14. f x 2 x 3 , 3 x 4 .

			0,	x 4
			0,	x 2
		2
	48.15. f x		(x 2), 2 x 5 .
	9		0,	x 5

118

									0, x 1
	48.16. f x	8 x 1 , 1 x																						3	.
																								2
													3
									0, x
												2
																			1
				0,						x
																	2
																											3
	48.17. f x	16 2x 1 ,												1				x											.
												2												4
																		3
				0,						x
																	4
				0,						x							1
																	4
											1															1
	48.18. f x	8 4x 1 ,													x													.
										4														2
																1
									0, x
																2
				0,						x 1
	48.19. f x		5			1 x4 , 1 x 1.
		8								x 1
				0,
				0,						x 0
	48.20. f x		6			x2 x , 0 x 1.
		5								x 1
				0,
				0,						x 0
				3
	48.21. f x							1 x2		, 0 x 1.
		4								x 1
				0,
				0,								x 0
						3
	48.22. f x								4 x2 , 0 x 4 .
		32
									0, x 4
				0,						x 0
				1
	48.23. f x							2x 1 , 0 x 2 .
		2								x 2
				0,

119

						0, x 0
48.24. f x			1		4x3 1 , 0 x 2 .
18						0, x 2
					0,	x 0
1
48.25. f x				sin x,		0 x .
		2
					0,	x
					0,	x
										2
		1
48.26. f x				cos x,				x							.
2						2								2
					0,	x
									2
					0,	x 0
48.27. f x 6 x x2 , 0 x 1.
					0,	x 1

0, x 0

48.28.f x 3 2x x2 , 0 x 2 .

4

0, x 2

0, x 1

48.29. f x 6 x2 x , 1 x 0 .
			0,	x 0
			0,	x 1
48.30. f x	7	1 x6 , 1 x 1.
12			0,	x 1
.						X
a 1	3 .
, X 3;7 .
.
P X		a				a
									.

120