Answer to Question #312936 in Calculus for bob

Question #312936

The acceleration of an object moving in a strange way has

been modelled as:


a = x ∙ e^x


Use integration by parts to find an equation to model the

velocity, v, given that v = ∫ x ∙ e^x dx


1
Expert's answer
2022-03-17T18:06:00-0400

v=xexdxv=\smallint{xe^{x}}dx


let p=xp=x and dr=exdxdr=e^{x}dx

=>dp=dx=>dp=dx and r=exr=e^{x}


pdr=prrdp\smallint{pdr}=pr-\smallint{rdp}


v=xexdx=xexexdxv=\smallint{xe^{x}dx}=xe^{x}-\smallint{e^{x}dx}


=>v=xexex+c=ex(x1)+c=>v=xe^{x}-e^{x}+c=e^{x}(x-1)+c





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