Let `S` be the area of the region enclosed by `y=e^-x^2,y=0,x=0,a n dx=1.` Then `Sgeq1/e` (b) `Sgeq1=1/e` `Slt=1/4(1+1/(sqrt(e)))` (d) `Slt=1/(sqrt(2))+1/(sqrt(e))(1-1/(sqrt(2)))`

Options

A. `Sge1/e`
B. `Sge1-1/e`
C. `Sle1/4(1+1/(sqrt(e)))`
D. `Sle1/(sqrt(2))+1/(sqrt(e))(1-1/(sqrt(2)))`

Answer

A, B, D

Explanation

`Sgt1/e` (As area of retangle `OCDS=1//e`)

Since `e^(-x^(2))ge e^(-x)AAx epsilon[0,1]`, we have
`S gt int_(0)^(1)e^(-x) dx=(1-1/e)`
Area of rectange `OAPQ+` Area of rectangle `QBRSgtS`
or `Slt 1/(sqrt(2))(1)+(1-1/(sqrt(2)))(1/(sqrt(e)))`
Since `1/4(1+1/(sqrt(e)))lt1-1/e`
Option 3 is incorrect.