Tsu-2011 - ieeetsu

2 2 2
()
D x f x dx .
asimetriis koeficienti a gamoiTvleba formuliT:
1
3
a ( x ) f ( x)
dx
3
.
eqscesis koeficienti e tolia:
1
4
e ( x ) f ( x) dx 3
4
.
magaliTebis amoxsnis nimuSebi:
magaliTi 1. uwyveti SemTxveviTi sididis ganawilebis simkvrivea:
2 x , Tu 1 x
2;
f
() x 3
0, sxvagan.
a). SeamowmeT, rom f () x akmayofilebs simkvrivis a) da b) Tvisebas;
b). gamoTvaleT P{1.5
2} .
x 0 ; garda amisa,
amoxsna. a). f( x) 0 yoveli x -saTvis, vinaidan 2 0
2 2 x 1
2 2
2 2 2
f
( x) dx xdx |
1
(2 1 ) 1.
1
3 3 2 3
2 2
2 x 2 1 2 2 1
1.5
1.5
3 2 3 3
b). N P{1.5
2} f ( x) dx |
(2 1.5 ) 1.75 0.583 .
3 x , roca
magaliTi 2. uwyveti SemTxveviTi sididis ganawilebis simkvrivea:
2
k(1 x ), Tu 1 x 1;
f
() x 0,
sxvagan,
sadac k mudmivia. ipoveT: a). k ; b). P{0.3
0.6} ; g). P{| | 0.2} .
amoxsna. a). visargebloT simkvrivis b) TvisebiT:
1
2 1 3 1
1 f
( x) dx k(1 x ) dx k( x x ) |
1
1
3
1 3 1 3 4 4 8k
k(1 1 ) k[( 1) ( 1) ] k k
( ) ,
3 3 3 3 3
e. i. 8 k 1 . saidanac k 3/8 ;
3
0.6
3 2 3 1 3 0.6
b).
P{0.3
0.6} (1 x ) dx ( x x )|
0.3
8 8 3
0.3
62