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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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