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JEE Advanced2007MathematicsIndefinite IntegrationActual

Let F(x) be an indefinite integral of ^2 x . Statement I The function F(x) satisfies F(x+ )=F(x) for all real x . Statement II ^2(x+ )= ^2 x for all real x .

Options

  1. AStatement I is true, Statement II is true; Statement II is a correct explanation for Statement I
  2. BStatement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
  3. CStatement I is true, Statement II is false
  4. DStatement I is false, Statement II is true

Correct answer

D. Statement I is false, Statement II is true

Step-by-step solution

aligned & F(x)= ^2 x d x= 1- 2 x 2 d x & F(x)= 1 4 (2 x- 2 x)+c aligned Since, F(x+ ) F(x) . Hence, Statement I is false. But Statement II is true as ^2 x is periodic with period .

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