Page 34 - Engineering Mathematics Workbook_Final

Calculus

2
(a) 4y (b) 16y 1 1
(c) (d)
6 12
(c) x (d) 8
−
2 xy dx dx =
176. The value of 0  1 x  2 x
172. Let
0   1 y xy sin xy 0   a b xy sin xy dy dx 3 1
1
( ) dx dy =
1
(a) a= 0, b = x (b) a = 1, b = x (a) (b)
8 6
(c) a = 0, b = 1 (d) a = -1, b = x 5 1
(c) (d)

173. For n N , the value of 24 2
 n 1− ( / x n ) n dx = 177. − 2 1  1+ x dx =
−
0 n x
(a) 3.5 (b) 5.5
(a) 0 (c) 4 (d) none

1 1 1 1
(b) 1+ + + ...+ 178. The integral 0  1 dx converges
2 3 n 1 x 2
−
to
1 1
(c) 1+ + ........+
2 n + 1 (a)  (b) 0
(c) / 2 (d) 
1 1
(d) 1+ + ........+ 1
2 n + 2 179. The integral  − 1 x 2 dx converges to

+
174. The value of  xy dx dy taken over
the region bounded by two axis and the (a) 0 (b) 
straight line x + y = 1 2

(c) − (d) 
1 1 2
(a) (b)
20 24
2
180. The area bounded by y = x and the
1 1 lines x = 0
(c) (d) 4 and y = is
30 40
64
0
175. If R is the region bounded by x = , (a) 64 (b) 3
y = 0 and x + y = 1 then 128 128
 R  ( x + 2 y 2 ) dx dy = (c) 3 (d) 4

1 1
(a) (b)
3 5

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