Let F(x) = _1^ x^2 t ,dt. STATEMENT-1: F'(x) = x. STATEMENT-2: If f(x) = _a^x (t) ,dt then f'(x) = (x).

JEE Advanced Mathematics question

Let . STATEMENT-1: . STATEMENT-2: If then .

(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 TrueCorrect

Answer: (D)

Solution

**Statement-2:** This is the Fundamental Theorem of Calculus (valid when is continuous, which is the intended setting). **True.** - **Statement-1:** By Statement-2 and the chain rule (Leibniz rule),

F'(x) =

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Question ID VK-110315