Answer to Question #312936 in Calculus for bob

Question

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

Answer 1

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

let $p=x$ and $dr=e^{x}dx$

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

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

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

$=>v=xe^{x}-e^{x}+c=e^{x}(x-1)+c$