# 21MAB102T Assignment 1

```SRM Institute of Science and Technology
Department of Mathematics
2022-2023 Even
Answer all questions (5 X 10 = 50 marks)
Assignment - 1
S.No.
1. Find the area inside the cardioid r = a(1+cosπ) and outside the circle π = π .
2. Evaluate β­ π₯π¦π§ππ₯ππ¦ππ§, where V is the volume given in the positive octant of the sphere
π
π¦2 + π§2 = 1 .
π₯2 +
3. Show that πΉΜ =(π§ 2 + 2π₯ + 3π¦)πΜ + (3π₯ + 2π¦ + π§)πΜ + (π¦ + 2π§π₯ )πΜ is irrotational but not solenoidal.
Hence find its scalar potential.
4. Verify Green’s theorem in a plane with respect to ∫ π₯ 2 ππ₯ − π₯π¦ππ¦ , where C is the boundary of the
πΆ
square formed by π₯ = 0, π¦ = 0, π₯ = π, π¦ = π .
5. Verify the Stoke’s theorem for πΉΜ = (π¦ − π§ + 2)πΜ − (π¦π§ + 4)πΜ − (π₯π§)πΜ over the surface of a cube
π₯ = 0, π¦ = 0, π§ = 0, π₯ = 2, π¦ = 2, π§ = 2 above the XOY plane.
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