25.

26.

20

28.

B1A005 Pages: 3

Module VI

Answer any 3 questions.

24. Verify Green’s theorem for ர்‌. (xy + ‏پورڈر‎ + x? dy where © is bounded by y = x and

y=x? (5)
Apply Green’s theorem to evaluate ‏.ل‎ (2x* — y?)dx + (x*+y?)dy = where © is the
boundary of the area enclosed by the x-axis and the upper half of the circle x? + y? = a?

(5)
Apply Stokes theorem to evaluate J. (x+y)dx + (2x-—y)dy + (y+z)dz whereC
is the boundary of the triangle with vertices (0,0,0), (2,0,0) and (0,3,0) (5)

Use Divergence theorem to evaluate ff; ۴۰7015۶ where F = xi + zj + yzk and 5 is the
surface of the cube bounded by x = 0, = 1, # = 0, ) = 1, 2 = Oand 2 = 1.Also verify
this result by computing the surface integral over S (5)

State Divergence theorem. Also evaluate ff; ೫-709 where F = மம்‌ + ‏بی + زط‎ and $

is the surface of the sphere x? + y? +27 = 1 (5)

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