Mathematics Division, School of Advanced Sciences and Languages
MATH-Calculus and Laplace Transform
Practice Set-2
============================================
Double integral
1. Verify that .
Ans.:
2. Evaluate the following integrals
..
Ans.:
Ans.:√12 Ans.:
(i) a
Z 1Z x 6
(e) (x2 + y2)dy dx.
.
0 x
ZZ 2 − 12x)dx dy where D = n(x,y)|0 ≤ x ≤ 4,(x − 2)2 ≤ y ≤ 6o 3. Evaluate
(42y
D
Ans.: 11136
ZZ 2 3
√
1
,4. Evaluate (2yx + 9y )dx dy where D is the region bounded byand y = 2 x.
Ans.:
5. Evaluate where D is the region bounded by x = −2y2 and x = y3.
Ans.:
6. Evaluate where D is the region bounded by y = 1 − x2 and y = x2 − 3.
Ans.: 0
7. Evaluate where D is the region bounded by and the y-axis.
Ans.:
8. Evaluate where D is the region bounded by
Ans.:
9. Evaluate where D is the region shown below.
Ans.: 36
RR
10. Evaluate ey4 dx dy where D is the region shown below.
D
2
, = 3 and the x-axis.
3
MATH-Calculus and Laplace Transform
Practice Set-2
============================================
Double integral
1. Verify that .
Ans.:
2. Evaluate the following integrals
..
Ans.:
Ans.:√12 Ans.:
(i) a
Z 1Z x 6
(e) (x2 + y2)dy dx.
.
0 x
ZZ 2 − 12x)dx dy where D = n(x,y)|0 ≤ x ≤ 4,(x − 2)2 ≤ y ≤ 6o 3. Evaluate
(42y
D
Ans.: 11136
ZZ 2 3
√
1
,4. Evaluate (2yx + 9y )dx dy where D is the region bounded byand y = 2 x.
Ans.:
5. Evaluate where D is the region bounded by x = −2y2 and x = y3.
Ans.:
6. Evaluate where D is the region bounded by y = 1 − x2 and y = x2 − 3.
Ans.: 0
7. Evaluate where D is the region bounded by and the y-axis.
Ans.:
8. Evaluate where D is the region bounded by
Ans.:
9. Evaluate where D is the region shown below.
Ans.: 36
RR
10. Evaluate ey4 dx dy where D is the region shown below.
D
2
, = 3 and the x-axis.
3
