Answer
$\displaystyle\int\limits_0^3(2\sin x-e^{x})dx=3-2\cos3-e^{3}$
Work Step by Step
$\displaystyle\int\limits_0^3(2\sin x-e^{x})dx$
Integrate each term separately and then apply the second part of the fundamental theorem of calculus to get the answer:
$\displaystyle\int\limits_0^3(2\sin x-e^{x})dx=2\int\limits_0^3\sin xdx-\int\limits_0^3e^{x}dx=-2\cos x-e^{x}\Big|_0^3=$
$...=-2\cos3-e^{3}+2\cos0+e^{0}=-2\cos3-e^{3}+2+1=...$
$...=3-2\cos3-e^{3}$