Page 35 - Engineering Mathematics Workbook_Final

Calculus

181. By change the order of integration (a) 0.27 (b) 0.67
0  2 x  2x ( , x y dy dx may be (c) 1 (d) 1.22
)
2 f
represented as 186. The function

)

2 f
(a) 0  2 x  2x ( ,x y dy dx f ( ) x =  x a sin 1 , x  0 is

x
)

(b) 0  2 y  y f ( ,x y dy dx  0 , x = 0

0
)
(c) 0  4 y  /2 y f ( , x y dy dx differentiable at x = for all al in the
interval
)
(d) x  2x 0  2 f ( , x y dy dx (a) (− ,1 ) (b) ( 1,− ) 
2
182. The volume generated by revolving the ) (d) ( ,1
area bounded by y = 8x and the line x (c) (1, )
2
= 2, about y-axis is [JAM CA 2006]

128 5 x
2
f
(a) (b) 187. Let ( ) x =  (t − 1 )(t − 5t + ) 6 dt ,
5 128 0
for all x R . Then
127 32
(c) (d)
5 5 (a) f is continuous but not differentiable
on R
183. The value of integral of the function
4
Q ( , x y = ) 4x + 3 10y along the (b) f’ is bounded on R
straight line segment from the point (0,0) (c) f’ has exactly three zeroes
to the point (1, 2) in the xy plane is
(d) f is continuous and bounded on R
(a) 33 (b) 34 [JAM CA 2011]
(c) 40 (d) 56 4
−
184. The value of 0   0   e − ( x + 2 y 2 ) dx dy = 188. For the function y = 1 x , the point
x =
0 is a point of
 (a) inflection
(a) (b) 
2 (b) minima

(c)  (d) (c) maxima
4

(d) absolute minima [JAM CA 2005]
2
185. The length of the arc y = x 3/2
3 189. The value of a and b for which the
3
2
f
between x = 0 and x = 1 is function ( ) x = x + ax + bx has

33