Question

Let F(x) be an indefinite integral of sin²x.

Statement-1: The function F(x) satisfies F(x + p ) = F(x) for all real x. because

Statement-2 : sin²(x + π) = sin² x for all real x.

(A)  Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

(B)  Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

(C)  Statement-1 is True, Statement-2 is False

(D)  Statement-1 is False, Statement-2 is True

Answer 1

Correct option  (D) Statement-1 is False, Statement-2 is True

Explanation :

we have

Hence, Statement-1 is false and Statement-2 is true because sin²x is periodic function with period π.