Page 41 - Engineering Mathematics Workbook_Final

Calculus

e − 1 e + 1 (d)  2/3 1 2 ( / 1 v− ) ( f u uv− ,uv )u du dv
(c) (d) 1/ (1 v− )
2 2
[JAM CA 2006]
[JAM CA 2005]
231. The area bounded by the curve
0  1 y  1 x y = (x + 2
227. The value of dx dy is ) 1 , its tangent at (1,4) and the
2
( x + y 2 ) x-axis is

  1 2
(a) (b) (a) (b)
4 2 3 3

  4
(c) (d) (c) 1 (d)
3 5 3

[JAM CA 2005] 232. If  denotes the region bounded by the
x-axis and the lines y = x and x = 1,
228. The value of the integral then the value of the integral

0   x   e − y dy dx cos 2x
( )
y   dx dy is
 x
(a) 0 (b) 1
sin2 cos2
(a) (b)
(c) 2 (d)  2 2

229. The entire area bounded by the curve (c) cos 2 (d) sin 2
r = a cos2 is
2
[JAM CA 2007]
(a) a (b) 2a
233. Let D be the region in the first quadrant


(c) a (d) 2 a lying between x + 2 y = 2 1 and
230. The double integral x + 2 y = 2 4. The value of the integral
1  2 x  2x f ( ,x y dy dx under the   sin ( x + y 2 ) dx dy is
)
2
transformation x u= (1 v− ), y uv is D
=
transformed into 
(a) (cos1 cos2− )

2
( / 1 v
−
(a)  1/2  2/3 1/ − − ) ) ( f u uv ,uv )du dv 4
(1 v
 − )
( / 1 v−
(b)  1/2  2/3 1/ 2 (1 v− ) ) ( f u uv− ,uv )u du dv (b) (cos1 cos4
4

( / 1 v−
(c)  1/2  2/3 1/ 2 (1 v− ) ) ( f u uv− ,uv )v du dv (c) (cos1 cos2− )
2

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