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

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​ F ( x ) = ∫ sin 2 x d x = ∫ 2 1 − cos 2 x ​ d x ⇒ F ( x ) = 4 1 ​ ( 2 x − sin 2 x ) + c ​ Since, F ( x + π )  = F ( x ) . Hence, Statement I is false. But Statement II is true as sin 2 x is periodic with period π .

Mathematics - Indefinite Integration Question with Solution | TestHub

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