evaluate the integral. ∫-3 to 1 e^u + 3 du

Answer:

$e + 12 - e^{-3}$

Explanation:

Step1: Aplicar la propiedad de la integral

$\int_{-3}^{1}(e^{u}+3)du=\int_{-3}^{1}e^{u}du+\int_{-3}^{1}3du$

Step2: Integrar $e^{u}$

$\int_{-3}^{1}e^{u}du = [e^{u}]_{-3}^{1}=e^{1}-e^{-3}$

Step3: Integrar la constante 3

$\int_{-3}^{1}3du = [3u]_{-3}^{1}=3\times1 - 3\times(-3)=3 + 9 = 12$

Step4: Sumar los resultados

$(e - e^{-3})+12=e + 12 - e^{-3}$