6. The acceleration of an object moving in a strange way has been modelled as $$ a=e^{x} x $$. a) Use integration by parts to find an equation to model the velocity $$ v $$ if $$ v=\int e^{x} x d x $$. b) Is the problem any different if you find $$ v=\int x e^{x} d x $$ ?

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For part (a), the velocity $$ v $$ can be modeled as $$ v = x e^{x} - e^{x} + C $$. For part (b), the integral $$ v = \int x e^{x} \, dx $$ leads to a more complex expression than $$ v = \int e^{x} x \, dx $$, but both represent the same physical quantity.

6. The acceleration of an object moving in a strange way has been modelled as \( a=e^{x} x \). a) Use integration by parts to find an equation to model the velocity \( v \) if \( v=\int e^{x} x d x \). b) Is the problem any different if you find \( v=\int x e^{x} d x \) ?

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6. The acceleration of an object moving in a strange way has been modelled as \( a=e^{x} x \). a) Use integration by parts to find an equation to model the velocity \( v \) if \( v=\int e^{x} x d x \). b) Is the problem any different if you find \( v=\int x e^{x} d x \) ?

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