Page 43 - Engineering Mathematics Workbook_Final

Calculus

0  1 1 y ) 242. The area of the region bounded by the
+
(c) − − f ( , x y dy dx
1 y
curves r = 1 and r = cos2 ,
3
)

−
+ −  0 1  − 1 y 2 2 f ( , x y dy dx 0    , is
−
2
1 y
)
+
(d) 0  1 − 1 y f ( , x y dy dx (a)  (b) 
−
1 y
2 3
)
−
− −  0 1  − 1 y 2 2 f ( , x y dy dx  
−
1 y
(c)
4 (d) 8
 
239. The value of x +  y dx dy , where
D [JAM CA 2010]
[x + y] is the greatest integer less than or
equal to x + y is the region bounded by x 243. The area included between the curves
2
= 0, y = 0 and x + y = 2, is x + 2 y = 2 a and
b x + a y = a b (a  0,b  ) 0 , is
2
2 2
2 2
2
3 1
(a) (b)
2 2  a
−
(a) a b
1 2
(c) (d) 0
4
(b)  a − 2 3ab b
+
2
2
x
240. The area bounded by the curves y =
(c) a a b −
and x = y is
2
2
2
(a) 1/3 (b) 2/3 (d)  a − b [JAM CA 2011]
(c) 4/3 (d) 5/3 244. The area bounded by the curves
−
[JAM CA 2009] x = 2 4 2y and x = 2 y + 4 is
241. The value of the integral (a) 16 (b) 24
0   /2 x   /2 sin y dy dx is (c) 30 (d) 36

y
245. The value of the integral
1    x x e − x 2 / y dy dx is
(a) 0 (b) 0 y= 0
2
(a) 0 (b) 1/2
(c) 1 (d) 2
(c) 4 (d) 1

[JAM GP 2005]

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