ENGGMATH 4 FINAL EXAM
SET C
I.Evaluate the ff. iterated integrals.
//2
tan x sec x
y cos xdydx
 


2. 
 cosx sin2y dx dy
3.   x e dy dx
1.
0
0
3 /2
0
2
7
/2
0
1 x2
y
0 0
4.

3
dx
0
( x  2) x  1
 / 2 1 / 3 1 cosy
  
5.
0
0
1- cosy
 / 2 cos x  - x
6.
  
7.

/6 0

3
x
xz dz dx dy
sin(x  y)dy dz dx
sin 3 y cos ydy
0
(2 x  3)dx
(3x  2)

x
9. 
dx
0
5 x  13
8.

10.
0
1
3

0
2
y 3 (4 - y 2 ) 3 dy
II. Find the area bounded by the curve y = x3 – 3x and the x-axis. Sketch
the curve indicating the area bounded.
III. The area bounded by the curve y = x3,
y = 0 & x = 1, is revolved about Oy. Find the volume generated. Sketch the
curve indicating the generating area.
IV. Find the area bounded by the given curves; y = 6x – x2 and y = x2 – 2x