GATE 2024 ST – Question 11

Calculus · Multiple Integrals · 1 mark · Multiple choice

D is bounded by y=x and y=4x−x². Find ∬_D x dxdy.

Show answer and explanation

Correct answer: (A) 27/4

Explanation

The curves meet at x=0,3, with the parabola above the line. Integrate ∫₀³x[(4x−x²)−x]dx=∫₀³(3x²−x³)dx=[x³−x⁴/4]₀³=27−81/4=**27/4, A**.

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