Find the area enclosed by the graph of `y=log_(e)(x+1),`y-axis, and the line y=1

Explanation

`y=log_(e)(x+1)`
`therefore" "x+1=e^(y)`
`rArr" "x=e^(y)-1`
From the figure, required area (Intergrating along y-axis)
`A=underset(0)overset(1)int(e^(y)-1)dy=[e^(y)-y]_(0)^(1)`
`=e^(1)-1-1+0`
`=e-2`
`"Also, "A=(e-1)xx1-overset(e-1)underset(0)intlog_(e)(x+1)dx=(e-1)-overset(e)underset(1)intlog_(e)x dx`
`=(e-1)-1=e-2`