QuestionCalculate the integral $\int_{0}^{2}\left(x^{2}+1\right) e^{-x} dx$.

Studdy Solution
Evaluate the equation at the limits of0 and2.
$$\int_{0}^{2}\left(x^{2}+\right) e^{-x} dx = -e^{-2} - e^{-2} +2e^{-2} -2 +0 - = -3e^{-2} -3$$The solution to the integral $\int_{0}^{2}\left(x^{2}+\right) e^{-x} dx$ is $-3e^{-2} -3$.