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A192001 Pages:3

Use triple integral to find the volume of the solid with in the

2

cylinder 2 + ~ = 4 and between the planes 7 = 0 and

1 + 2 = 3.
Module V

Answer any three questions, each carries 5 marks.
17 = ‏ع + 2 +ع‎ 20047 = |1|, prove that V2r" =n(n + 1) 72

E 2 2

ivaluate ‏إل‎ (3x? + ೫3) dx + 2xydy along the curve

C:x =cost,y =sint,0< 0

Find the scalar potential of F = (2xy+ ‏33ج‎ +x27+3xz2k

Find the work done byF(z,y) = (x+y)i+ xy ‏ز‎ - 22 ¢ along the line
segments from (0,0,0) 10 (1,3, 1) to (2,-1, 5)

Show that i; e*siny dx +e* cosy dy 15 independent of path

Hence evaluate 7 e*siny dx + €= cosy dy

Module VI

Answer any three questions, each carries 5 marks.
Evaluate using Green’s theorem in the plane | («?dx - xydy)where

C is the boundary of the square formed by x = 0.3 = 0 = 2.3 =a
Evaluate the surface integral ff f(x y,z)ds where

f(x, y,z)=x+y, ೮ is the portion of the surface z = 6 - 2x — 4y in

the first octant.

Using divergence theorem find the flux across the surface ச which
is the surface of the tetrahedron in the first octant bounded by

x + + 2 = 1 and the coordinate planes, F = (x? + y)i+ ‏ہر‎ - (2x2 + yk
Evaluate | (e*dx + 2ydy ~ dz)where Cis the curve நு? =4,2 = 2
using Stoke’s theorem

Evaluate the surface integral ff f(x,y,z) च where

f(x 9, 2) = 2 + 97, 6 15 16 surface of the sphere x?+ y? + 22 =a?

Gon OF ENGINEER,

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