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GATE 2020 CE (CE1) – Question 14

Engineering Mathematics · Calculus: Integrals, partial and total derivatives, gradient, divergence, curl, line, surface and volume integrals · 1 mark · Multiple choice

Find area enclosed by $x^2/a^2+y^2/b^2=1$.

  1. $\pi ab/4$
  2. $\pi ab/2$
  3. $\pi ab$
  4. $4\pi ab/3$

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Show answer and explanation

Correct answer: (C) $\pi ab$

Explanation

Transform the unit disk by $x=au$, $y=bv$. The area Jacobian is ab, so area is ab times the unit-disk area π: **$\pi ab$, C**.