Question

How do you determine if the improper integral converges or diverges `e^(-2t) dt` from negative infinity to -1?

Answer 1

The integral is divergent

Explanation:

The improper ntegral is

`I=int_x^-1e^(-2t)dt`

`=[-1/2e^-(2t)]_x^-1`

`=[1/2e^(-2t)]_-1^x`

`=1/2e^(-2x)-1/2e^2`

Therefore,

`lim_(x->-oo)I=lim_(x->-oo)(1/2e^(-2x)-1/2e^2)=+oo`

The integral is divergent