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"If " int x e^(x) cosx dx=ae^(x)(b(1-x)s...

`"If " int x e^(x) cosx dx=ae^(x)(b(1-x)sinx+cx cosx)+d,` then

A

`a=1,b=1,c=-1`

B

`a=(1)/(2),b=-1,c=1`

C

`a=1,b=-1,c=1`

D

`a=(1)/(2),b=1,c=-1`

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int xe^(x)cosx dx `
`=xe^(x)sinx-int(xe^(x)+e^(x))sinx dx `
`=xe^(x)sinx-xe^(x)(-cosx)-int(xe^(x)+e^(x))cosx dx-int e^(x)sinx dx `
`=xe^(x)sinx+xe^(x)cosx-int xe^(x) cosx dx -int e^(x)(cosx+sinx)dx`
`"or " 2I=xe^(x)(sinx+cosx)-e^(x)sinx+d`
`=e^(x)((x-1)sinx+xcosx)+d`
`"or " I=(1)/(2)e^(x)((x-1)sinx+xcosx)+d`
`"or "a=(1)/(2),b=-1,c=1`
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