Calculus Homework Help

Question

Determine whether the integral is convergent or divergent.

∞

e−1/x / x2 dx

3

If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.)

Answer 1

let u = -1/x

then

integral of e^(-1/x) = e^u

= e^u + c

= e^(-1/x) + c

as x approaches infinity, -1/x approaches 0 and e^(-1/x) approaches 1

it converges to 1 + c