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NSA192001 Pages:4

Evaluate ‏ملا‎ ೫ மட dy where ಔ is the region bounded by the parabolas

y? = 4x and x* = 4y.

Use double integral to find the area of the region enclosed between the

2
parabola y= = and the line ‏پر‎ = 2x.

21 2
Evaluate 1 [€ 2൧ by reversing the order of integration
02
2
Use triple integrals to find the volume of the solid within the cylinder
x? + y? = 9 and between the planes Z= Landx+z=5.

Module-IV

: ⋅ ↧⋅∑↿⋅⋅≻↼⋅∍∙⊋⋅⋅∆
Find the general term of the series 1+ + + 123 ⊹⋅⋅⋅⋅∙∙⋅ and use
1.3 1.3-5 ٦٣۶+

the ratio test to show that the series converges.

Test whether the following series is absolutely convergent or conditionally

०० (- iy

convergent 2,

k=l J ktk + 1)
x x? ഥ്‌ xk
Test the convergence of ⊹⋅−∙⋅⋯⋯ +--------
1.2 2.3 3.4 k(k + 1)
2 (641
Test the convergence of the series > ൮).
k=l 4tk!4
Module-V
Find the Fourier series of periodic function with period 2 which is given
below f(x) ‏ہے سی‎ H that 14-44 ಸ
ow (> = . Hence prove tha ---+--+---=-
١ ೫; 05೫5! 7 eS 8

kx Ok(L-x) L/2
ತಾ
4,
19
2)

Find the half range cosine series for f(x) = |

NCS

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