What is #f(x) = int xe^x# if #f(2)=3 #?

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Answer 1 · 2018-03-05T15:08:46

#f(x)=xe^x-e^x+3-e^2#

#f(x)=intxe^xdx, f(2)=3#

#f(x)=intu(dv)/(dx)dx=uv-intv(du)/(dx)dx#

in this case

#u=x=>(du)/(dx)=1#

#(dv)/(dx)=e^x=>v=e^x#

#:.f(x)=xe^x-inte^xdx#

#f(x)=xe^x-e^x+c#

# f(2)=3#

#:. f(2)=3=2e^2-e^2+c#

#c=3-e^2#

#f(x)=xe^x-e^x+3-e^2#