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GATE 2026 ME – Question 11

Engineering Mathematics · Calculus: Definite and improper integrals, double and triple integrals · 1 mark · Multiple choice

Domain $A$ is bounded by curve $x^2 = 4y$, ordinate $x = 2$, and $x$ axis. The value of $\iint_A y\,dx\,dy$ is

  1. 1/5
  2. 1/3
  3. 5/12
  4. 1/2

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Correct answer: (A) 1/5

Explanation

For $x$ from 0 to 2, $y$ runs from 0 to $\frac{x^2}{4}$. The inner integral is $\int_0^{x^2/4} y\,dy = \frac{x^4}{32}$. Then $\int_0^2 \frac{x^4}{32}\,dx = \frac{32/5}{32} = \frac{1}{5}$.