Let f(x)=1x6+x4 and F be a antiderivative of f such that F(1)=π4+23Statement-1 F13=π6Statement-2: F(x)=tan−1⁡x+13x−1x3

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STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation forSTATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is False

STATEMENT-1 is False, STATEMENT-2 is True

answer is C.

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Detailed Solution

f(x)=1x4x2+1=1x4−1x2+1x2+1So F(x)=−13x3+1x+tan−1⁡x+CF(1)=23+π4+Cso C=0F(x)=tan−1⁡x+1x−13x3⇒F13=π6.

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