Let f(x) be an indefinite integral of ^2x. Consider the following statements : Statement 1 : The function f(x) satisfies f(x+ )=f(x) for all real x. Statement 2 : ^2(x+ )= ^2x for all real x. Which one of the following is correct in respect of the above statements?

NDA 2017 Mathematics question

Let be an indefinite integral of . Consider the following statements : Statement 1 : The function satisfies for all real x. Statement 2 : for all real x. Which one of the following is correct in respect of the above statements?

(A)Both the statements are true and Statement 2 is the correct explanation of Statement 1
(B)Both the statements are true but Statement 2 is not the correct explanation of Statement 1
(C)Statement 1 is true but Statement 2 is false
(D)Statement 1 is false but Statement 2 is trueCorrect

Answer: (D)

Solution

, so \dfrac{π}{2}$≠

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Question ID VK-028656