Mavzu: Xosmos karrali integrallar reja: kirish i-bob. Xosmas integrallar

Yechish:

2

3

x ^3  3 1 

1

3 1 

1

1  x

2

2

2

f

( x )





x



x

x ^2  1

1

1

1 ;

x 2

1 

x ^3 1 

x 2

x 2

1		3 1					1						1
							x ^2		1
													f ( x )  1 ; ^ ^		 1
x ^3		 f ( x ) 
											; li m x ^3
								1
		1									x 		3
								x ^2

Demak, berilgan xosmas integral uzoqlashadi.


3.  e ^ ^x ^2	d x	integral tekshirilsin.
0

Yechish: f ( x )  e ^{ x 2} ; Lopital qoidasiga asosan 0 da ^{li m}
x 

bo ‘ladi. Xususiy holda  21bo ‘lganda,

li m x ²  e ^{ x 2} 0,bo ‘ladi. Demak, berilgan integral yaqinlashadi.

x 


x ^  e ^{x 2}  0 ,

Bu Puasson

integrali bo ‘lib, uning qiymati									ga teng.
							2
				
	
				;  e ^ ^x ^2 d x 
 e ^ ^x ^2 d x 					
	2
0				