How do you evaluate the definite integral #int cosxe^sinx# from #[0, pi/2]#?

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Answer 1 · 2016-10-18T08:07:41

#e-1#

#int_o^(pi/2)cosxe^sinxdx#

recognising that # d/(dx)(e^sinx)=cosxe^sinx #

we have

#int_o^(pi/2)cosxe^sinxdx=[e^sinx]_0^(pi/2)#

#=e^sin(pi/2)-e^sin0#

#=e^1-e^0#

#=e-1#