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JEE Main2013MathematicsDefinite IntegrationActual

If x= ₀^y d t 1+t^2 , then d^2 y d x^2 is equal to :

Options

  1. Ay
  2. B1+y^2
  3. Cx 1+y^2
  4. Dy^2

Correct answer

A. y

Step-by-step solution

x= ₀^y d t 1+t^2 1= 1 1+y^2 d y d x [ . If I (x)= _ (x) ^ (x) f(t) d t , then d I (x) d x =f (x) dy dx = 1- y ^2 d^2 y d x^2 = 1 2 1+y^2 2 y d y d x = y 1+y^2 1+y^2 =y

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