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Question

y=f(x) is a function which satisfies (i)f(0)=0
(ii) f′′(x)=f(x) and (iii) f(0)=1
then the area bounded by the graph of y=f(x) the lines x=0,x1=0 and y+1=0 is

A
e
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B
e2
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C
e1
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D
e+1
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Solution

The correct option is B e1
If f(x)=x+cf(x)=kex
f(x)=ex {f(0)=1k=1}
f(x)=ex+λ
f(x)=ex1 {f(0)=0λ=1}
A=10(ex1+1)dx=e1

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