Question

Find the area under the curve y=5xe^{-x} for x ≥ 1

Answer 1

Have you learned integration by parts?

Answer 2

Actually, do you know improper integral?

Answer 3

Never mind my last comment.
If you know limit, you should be fine while I take you step by step.

Answer 4

First, let's find a general formula for the area under curve in the interval [1,t]

Answer 5

\[\int\limits_{1}^{t}5xe^{-x}\]

Answer 6

Now, as @TanteAnna asked, do you know integration by parts?

Answer 7

\[\int\limits_1^{\infty } 5 x e^{-x} \, dx=\frac{10}{e} \]

Answer 8

Thanks guys