How do you find the definite integral of #(e^sin(x))cos(x) dx# from #[0, pi]#?

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Answer 1 · 2016-07-05T11:42:01

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well you need to spot the pattern that flows from the chain rule

#(e^{f(x)})^prime = f'(x) e^{f(x)}#

and here #f = sin x#

so #int_0^pi dx qquad e^sin(x)cos(x) #

#= [ e^sin(x)]_0^pi #

#= [ e^sin(pi)] - [ e^sin(0)] #

#= 1-1 = 0#

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