Let F(x) be an indefinite integral of sin2x.STATEMENT-1 The function F(x) satisfies F(x+π)=F(x) for all real x. because STATEMENT-2: sin2(x+π)=sin2x for all real x.
A
statemenstatement -1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
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B
Statement-1 is True, Statement-2 is True; Statement-2 is Not a correct explanation for statement-1
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C
statement - 1 is True, Statement - 2 is False
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D
Statement - 1 is False, Statement- 2 is True
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Solution
The correct option is C Statement - 1 is False, Statement- 2 is True f(x)=∫sin2xdx=12∫(1−cos2x)dx=12(x−12sin2x)+c ∴f(x+π)≠f(x) ∴ Statement 1 false Statement2:sin2(x+π)=sin2x is true ∀x∈R