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MHT CET202617 April 2026Evening ShiftMathematicsDifferentiationActual

If y = x^2 + x^2 + x^2 + and dy dx = f(x) 2y - 1 then, f(x) , dx =

Options

  1. Ax^2 + c
  2. B- x^2 + c
  3. Cx^2 + c
  4. D- x^2 + c

Correct answer

C. x^2 + c

Step-by-step solution

Given y = x^2 + x^2 + x^2 + Squaring both sides: y^2 = x^2 + y Differentiating both sides with respect to x : 2y dy dx = -2x x^2 + dy dx (2y - 1) dy dx = -2x x^2 dy dx = -2x x^2 2y - 1 Comparing with dy dx = f(x) 2y - 1 : f(x) = -2x x^2 Evaluating the integral: f(x) , dx = -2x x^2 , dx Substituting x^2 = t 2x , dx = dt : - t , dt = t + c f(x) , dx = x^2 + c Answer: x^2 + c

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