Determine if convergent or divergent:
Integral 1 to infinity of e to the power of (-1/2).
You integral does not make a lot of sense to me. e^(-1/2) is a constant, no variable.
INT 1/sqrte dx from 1 to inf is
1/sqrte * (infinity-1)
I suspect you meant something else.
sorry if i was not clear. it is
INT 1/sqrt e (the constant) dy from 1 to infinity.
Determine if it is convergent or divergent
To determine if the integral ∫1 to infinity of e^(-1/2) converges or diverges, we need to evaluate the integral.
First, let's calculate the integral:
∫(1 to infinity) e^(-1/2) dx
We can use a basic integration rule to evaluate this integral:
∫ e^(-1/2) dx = -2e^(-1/2)
Now, let's calculate the definite integral from 1 to infinity:
∫(1 to infinity) e^(-1/2) dx
= lim (t -> infinity) ∫(1 to t) e^(-1/2) dx
= lim (t -> infinity) [-2e^(-1/2)] evaluated from 1 to t
= lim (t -> infinity) [-2e^(-1/2) - (-2e^(-1/2))]
= lim (t -> infinity) [-2e^(-1/2) + 2e^(-1/2)]
= lim (t -> infinity) 0
= 0
Since the value of the definite integral is zero, the integral converges.
Therefore, ∫1 to infinity of e^(-1/2) converges.