Answer
$a)\int e^{\sin x}\cos xdx=e^{\sin x}+c$
$b)\int ^{2}_{0}e^{\sin x}\cos xdx=e^{\sin 2}-e^{\sin 0}\approx 1.48 $
Work Step by Step
$u=\sin x\Rightarrow du=\cos xdx\Rightarrow $
$$a)\int e^{\sin x}\cos xdx=\int e^{u}du=e^{u}+c=e^{\sin x}+c$$
$$b)\int ^{2}_{0}e^{\sin x}\cos xdx=e^{\sin x}]^{2}_{o}=e^{\sin 2}-e^{\sin 0}\approx 1.48 $$
