Answer
$$1$$
Work Step by Step
The area is given by $A=\int_0^{10} xe^{-x} \ dx$
We will solve the given integral by using integrate-by-parts formula such as: $\int udv=uv-\int v du$
Here, $u=x$ and $dv=e^{-x} dx \implies v=-e^{-x}$
$\displaystyle \int_0^{10} xe^{-x} \ dx=x(-e^{-x})-\int_0^{10} (-e^{-x}) \ dx$
or, $=[-x e^{-x} -e^{-x}]_0^{10}$
or, $=[-10 e^{-10} -e^{-10}]-[0 - e^{0}]$
or, $=-11 e^{-10} +1$
Therefore, the required area is: $Area \approx 1$
