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GATE 2022 MA – Question 45

Calculus · Vector Calculus · 2 marks · Multiple choice

Find work of F=(x+y)i−(x²+y²)j along the upper unit semicircle from (1,0) to (−1,0).

  1. −π
  2. −π/2
  3. π/2
  4. π

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Correct answer: (B) −π/2

Explanation

Parametrize x=cos t,y=sin t for 0≤t≤π. On the circle x²+y²=1. The work integrand is −cos t sin t−sin²t−cos t. The first and third terms integrate to zero; ∫₀^πsin²t dt=π/2. Work=**−π/2, B**.

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