The value of `int_0^1e^x^(2-x)dx` is `<1` (b) `>1` (c) `> e^(-1/4)` (d) `<e^(-1/4)`

Question

The value of `int_0^1e^x^(2-x)dx` is `<1` (b) `>1` (c) `> e^(-1/4)` (d) `A. `lt1`
B. `gt1`
C. `gte^(-1/4)`
D. `lte^(-1/4)`

Answer 1

Correct Answer - A::C
`int_(0)^(1)e^(x^(2)-x)dx`
For `x epsilon(0,1),x^(2)-x epsilon(-1//4,0)`
`:.e^(-1//4)lt e^(x^(2)-x)lte^(0)`
or `e^(-1/4)lt int_(0)^(1)e^(x^(2)-x)dxlt1`