`y=f(x)` is a function which satisfies `f(0)=0, f"''(x)=f'(x)` and `f'(0)=1` then the area bounded by the graph of `y=f(x)`, the lines `x=0, x-1=0` and `y+1=0` is

Options

A. e
B. e-2
C. e-1
D. e+1

Answer

3

Explanation

`(f'(x))/(f'(x))=1`
"integrating"
"ln (x) = x+c`"
`f'(x)=e^(x)`
`f(x)=e^(x)-1`
`"Area" = overset(1)underset(x)int (e^(x)-1)dx`
`=e^(x)overset(1)underset(0) = e-1` `(f'(x))/(f'(x))=1`
"integrating"
"ln (x) = x+c`"
`f'(x)=e^(x)`
`f(x)=e^(x)-1`
`"Area" = overset(1)underset(x)int (e^(x)-1)dx`
`=e^(x)overset(1)underset(0) = e-1`