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Q.

Let f(x)=xex(1+x)2,x≠−1 Statement-1: The antiderivative F of f (x) satisfying F(0)=1is 11+xexStatement-2: f (x) is of the form g(x)+g′(x)ex for some g(x).

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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 forSTATEMENT-1

c

STATEMENT-1 is True, STATEMENT-2 is False

d

STATEMENT-1 is False, STATEMENT-2 is True

answer is A.

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Detailed Solution

F(x)=∫xex(1+x)2dx=∫11+x−1(1+x)2exdx=11+xex+CF(0)=1⇒C=0 so F(x)=11+xex.

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