Page 51 - Engineering Mathematics Workbook_Final

Calculus

2
2
(x + 1 + ) 1 = 2 . The integral 308. The double integral
) ( y −
evaluates to   1 2 x 2x f ( , x y )dy dx under the

17
=
(a) 17 2 (b) transformation x = ( 4 1 v− ) , y uv is
2
transformed into
2
(c) (d) 0 2/3 ( 2 1 v− )
17 (a)  1/ 2  1/ (1 v− ) ( f u uv− ,uv )du dx
2/3 2 ( / 1 v )
−
−
(b)  1/ 2  1/ − ) ( f u uv ,uv )du dx
(1 v
  − 2 2 ) )
−
306. The value of   e ( x + y dxdy = (c)  1  2 ( / 1 v ( f u uv ,uv )u du dx
−
(1 v
0 0 2/3 1/ − )
−
 (d)  2/3  2 ( / 1 v ) ( f u uv ,uv )u du dx
−
(a) (b)  1/ 2 1/ − )
(1 v
2
 309. By change the order of integration
(c)  (d)
4  2 2x f ( ,x y )dy dx may be represented
2 
307. The evaluate the double integral 1 x
as
)+
y
8  ( / 2 1  2x y  − 
     dx dy , we make the 2 2x

)
  2   (a)   f ( , x y dy dx
0  y / 2 
0 x 2
 2x −  y y y
substitution u =   and v = . 2
)
 2  2 (b)   f ( , x y dy dx
0 y
The integral will reduce to
4 y
)
4  2  (c)   f ( ,x y dy dx
 

(a)    2udu dv
0  0  0 y / 2
x
2 2
)
4  1  (d)   f ( ,x y dy dx [GATE]
 

(b)    2udu dv x 2 0
0  0 
310. Changing the order of the integration
4  1  in the double integral
 
(c)    udu dv

0  0 
4  2 
 

(d)    udu dv [GATE-14-EE-SET2]
0  0 

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