Annamalai University 2008-2nd Year B.Sc Mathematics " 640ANALYSIS - II " (PART - III - A - I - MAIN ) ( ) ( - II ) 5232 - Question Paper

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Name of the Candidate :

5 2 3 2 B.Sc. DEGREE EXAMINATION, 2008

(MATHEMATICS)

(SECOND YEAR)

(PART - III - A -1 - MAIN)

(PAPER - II)

640. ANALYSIS - II

(Including Lateral Entry )

December ]    [ Time : 3 Hours

Maximum : 100 Marks

Answer any FIVE questions.

Each question carries TWENTY marks.

(5 x 20 = 100)

1. Evaluate : (a)

Ix + m ax + b

3x² + 4x + 7

x² x + 2

(4x5 = 20)

2. (a) Prove that

( a + b - x) dx

and hence evaluate

( n - 1 ) 7t/n

a

x sin x dx

71 / X

(b) Prove that f⁷¹

log (1 + cosx) dx = 71 log (1/2)

(b)    Solve:

z = px + qy + 2-pq

(c)    Solve :

( x² - yz ) p + (p² - zx ) q = z² - xy

( 6 + 6 + 8 )

(c) Solve :

(D² + 16 ) y = 2 e^-3x + cos 4x

( 6 + 6+ 8 )

9. (a) Solve :

(D² + 4D + 5 ) y = e^x + x³ + cos 2x

(b) Solve:

(1-x)p + (2-y)q=3-z

10 (a) Solve :

P ( 1 + q²) = q ( z - 1 )

where

dz

^{P =} 3T ^;

dz

^q " 5y

prove that

(b) Find a reduction formula for x¹¹¹

dx

(log x)^x

(10 + 10)

4.    (a) Prove that every continuous function is

integrable.

(b) If f (x) is integrable in (a, b), prove that I f (x) I is integrable in (a, b).

(10 + 10)

5.    (a) Find the area of the ellipse

*² ₊ 4 . .

y = c cosh e

from the origin to the point (x, y).

(10 + 10)

6. (a) Find the moment of inertia of a hollow sphere about a diameter.

(b) Evaluate

dx dy dz (x + y + z+ l)^;

taken over by the volume bounded by the planes

x = 0,

y = 0,

z = 0,

dy y+ 2

dx x-1

(b) Solve:

dy x² + 3y² dx 3x² + y²

(c) Solve :

dy

x = (x + 1) sec y dx

( 7 + 7 + 6 )

8. (a) Solve

(x² + y²) (xdx + ydy)

(b) Solve:

d²y dy

- 4 __ + 4y = 0

dx² dx

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Attachment: annamalai-university-2008-b-sc-mathematics-16700-1.pdf

Earning:   Approval pending.