How do you evaluate the definite integral #int e^(sin(x))*cosx dx# from #[0,pi]#?
1 Answer
Mar 26, 2016
Explanation:
We have
#int_0^pie^sinxcosxdx#
If we let
We will want to change the bounds by plugging the current bounds into our
#u(0)=sin(0)=0#
#u(pi)=sin(pi)=0#
Notice that something fairly odd has happened--both our bounds have become
#=int_0^0e^udu#
When both the bounds of an integral are the same, the integral's value is
Recall that the integral just finds the area under a curve--there is no area if we are traveling from