Page 49 - Engineering Mathematics Workbook_Final

Calculus

12 5 295. The volume generated by revolving
2
2
(a)  a (b)  a
5 12 the area bounded by y = 8x and the
2
6 5
−
2
2
2
(c)  a (d)  a line x = , about y axisis
5 6
128 5
292. The surface area of the solid (a) (b)
5 128
generated by revolving line segment
127 32
y = x + 2 for 0  x  1about the line (c) 5 (d) 5
y = 2 is __________

(a) 2 (b) 2

2
(c) 2 2 (d) 2 296. The area bounded by x = 2y and
=
2

293. If the line y mx, 0 x  2 is y = 2x is _______
rotated about the line y = − 1 then the 1 2
(a) (b)
area of the generated surface is 3 3
4
_________ (c) (d) 4
3
+
+
(a) 4 (1 m ) 1 m
297. The area between the parabolas
+
+
4
(b) ( 1 m 2 ) 1 m y = 4ax and x = 4ay is
2
2
2
+
2
(c) 4 ( 1 + m ) 1 m (a) a (b) 14 a
2
2
3 3
2
+
+
(d) 4 (1 m ) 1 m 16 17
2
2
(c) a (d) a
3 3
294. The volume generated by revolving
[EE, ESE-2019]
the area bounded by the parabola
298. The area of the region bounded by the
y = 2 8 , x y axis and the lines y = − 4 to
−
parabola y = x + 2 1and the straight
y = 4 about y-axis is
line x y+ = 3 is
32
(a) 32 (b) 59 9
5 (a) (b)
128 6 2
(c) (d) None of the above 10 7
5 (c) (d)
3 6
[EE-1994]

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