18

19

20

b)

a)

b)

a)

b)

a)

b)

a)
b)

01MAT101121903-B

Find the mass and centre of gravity of the lamina in the first quadrant bounded

by the circle ೫೨ + क? = 1 and the coordinate planes with density function xy.

Module-IV
5 (6-1 k+2
Test the convergence 0) 032
tak + 1) + 2Xk +3( 2-1
Test whether the following series is absolutely convergent or conditionally
00 (- 1)“
convergent
2 Jk(k + 1)

1.3 3.5 । 1.3.5.7
1.2 123 4

Test the convergence of the series 1+

ಊಉ
Test the convergence: (i >=
k=l

Module-V

2x
|+ --, -7 < <0
Find the Fourier series of / (20) = a

1-—,07

Obtain Fourier series of ச” the interval (—1,1)
Find the Fourier series f(x) = x? — 2 ‏مذ‎ the interval (—2,2)

Find the Fourier cosine series of f(x) = x” 110 < x >> गा.

Page 3 of 3

முத்‌ വിച്ച്‌;

2k +3

(7)

(7)

(7)

(7)

(7)
(7)

(7)
(7)