16 a)

17 a)

ات

)

18 a)

b)

19 a)

20 a)

b)

0000MAT101121904

Find the mass and center of gravity of the triangular lamina with vertices

(0,0), (0,1) and (1,0) and density function d(x, y) =xy

Evaluate ‏ہلا‎ x? dy dx,whereR is the region between y=X and y=x*

Module-IV

Discuss the convergence of the series

لا ‎ek‏ !<
کے دی 002

Examine the convergence and divergence of the series

1.3 1.3.5 1.3.5.7
Test the convergence of 1+ 3 + य + : +

3! 3! 7!

०० k 1 -2)
Prove that the series 2, (- 1) ர்‌ k(k+1) is conditionally convergent.

Module-V

Obtain Fourier series for the function f(x) = |sin x| -7 < <

7
kx; 0> ×>

If ‏(د)‎ = 2 then show that
k(a-x) ; > > 7

4k sinx 5113. ‏۶ء‎
‎+) =—(— ~
70 4 1 3 ട്‌

Find the Fourier cosine series of ‏7ر‎ (x)=x° in (0൬. Hence show that

Find the Fourier series for the function
f(x) = 0> <> 1
= ‏#د-1‎ l
Page 3 of 3

(7)

(7)

(7)

(7)

(7)

(7)

(7)

(7)

(7)

(7)