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JEE Main2012MathematicsIndefinite IntegrationActual

Let f(x) be an indefinite integral of ^3 x . Statement 1: f(x) is a periodic function of period . Statement 2: ^3 x is a periodic function.

Options

  1. AStatement 1 is true, Statement 2 is false.
  2. BBoth the Statements are true, but Statement 2 is not the correct explanation of Statement 1.
  3. CBoth the Statements are true, and Statement 2 is correct explanation of Statement 1.
  4. DStatement 1 is false, Statement 2 is true.

Correct answer

D. Statement 1 is false, Statement 2 is true.

Step-by-step solution

Statement -2: ^3 x is a periodic function. it is a true statement. Statement-1 Given f(x)= ^3 x d x aligned & = ( 3 x 4 + 3 x 4 ) d x & = 1 4 3 x 3 + 3 4 x & = 1 12 3 x+ 3 4 x aligned Now, period of 1 12 3 x= 2 3 Period of 3 4 x=2 Hence period of f(x)= L.C.M. (2 , 2 HCF of (1,3) = 2 1 =2 Thus, f(x) is a periodic function of period 2 . Hence, Statement -1 is false.

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