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Question Number 75082 by Rio Michael last updated on 07/Dec/19

find ∫_0 ^π e^(cosx) sinx dx

find∫0πecosxsinxdx

Answered by mr W last updated on 07/Dec/19

∫_0 ^π e^(cosx) sinx dx =−∫_0 ^π e^(cosx) d(cos x) =−[e^(cos x) ]_0 ^π =e−(1/e)

∫0πecosxsinxdx=−∫0πecosxd(cosx)=−[ecosx]0π=e−1e

Commented by Rio Michael last updated on 07/Dec/19

i don′t understand step 2 sir

idon′tunderstandstep2sir

Commented by MJS last updated on 07/Dec/19

it′s short for ∫_0 ^π e^(cos x) sin x dx= [t=cos x → dx=−(dt/(sin x))] =−∫_1 ^(−1) e^t dt=[−e^t ]_1 ^(−1) =[e^t ]_(−1) ^1 =e−(1/e)

it′sshortfor∫π0ecosxsinxdx=[t=cosx→dx=−dtsinx]=−∫−11etdt=[−et]1−1=[et]−11=e−1e

Commented by Rio Michael last updated on 07/Dec/19

thank you sir,thank you so much sir

thankyousir,thankyousomuchsir

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