STATEMENT-1: _0^ /2 dx 1 + ^3 x = 4 . STATEMENT-2: _0^a f(x) ,dx = _0^a f(x + a) ,dx where f(x) is an integrable function.

JEE Advanced Mathematics question

STATEMENT-1: . STATEMENT-2: where is an integrable function.

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

Answer: (C)

**Statement-2:** Put : , which in general differs from . Counter-example: , : but . **False.** (The correct property is $ f(x) dx = f(a -

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Question ID VK-110314