15.9
Change of Variables in Multiple Integrals
◎ 單選擇題
1.
, ,
The volume of the solid
,
(A)
1 is
(C) π,
,
(D)
for which the value of the triple integral
be a region in
1
is a maximum . Then
(A)
, ,
(B)
(C)
, ,
1
, , ∅ |0
(D)
, ,
Ans: B
1
1,
√
2
0
2
3
is
,
√
3
√
1,0
2 ,
√
;
3 ,2
3
1;
;
√
.
[103 學年度]
(A) ;
(B) ;
|
|
(C) 2;
(D) .
,
|
1 is
03 學年度]
4. The value of the double integral ∬
0,2 , 1,1 , 2,2 and 1,3 , is
(A) ln 2 ;
(B) 2 ln 2 ;
Ans: A [104 學年度]
, where
(A) ;
(B) ;
[105 學年度]
is the square with verties
(C) 3 ln 2 ;
(D) 6 ln 2 .
=
5. The iterated integral
Ans: C
√
1 2
2 ,0 ∅
1, 0
3. The area of the region
Ans: B
.
[102 學年度]
Ans: B
2.
(B)
|
(C) 1
;
(D) 1
.
6. The triple integral ∭
(A) π;
(B) π ;
Ans: B [105 學年度]
(C) π ;
(D) π .
◎ 填空題
1. Let R be the square with vertices (0,0), (1, 1), (1, 1) and (2,0). Then
Ans: 0 [103 學年度]
2.
double integral
sin
___________
where
is the parallelogram with successive vertices
, 0 , 2 , , , 2 and 0, .
Ans:
[105 學年度]