# What is #f(x) = int (3-x)e^x dx# if #f(0)=-2 #?

So, taking it as such, we get the answer as given above.

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The function ( f(x) = \int (3 - x)e^x , dx ) evaluates to ( f(x) = (2 - x)e^x + C ), where ( C ) is the constant of integration. Given that ( f(0) = -2 ), we can find ( C ) by substituting ( x = 0 ) into the function. This yields ( -2 = (2 - 0)e^0 + C ), which simplifies to ( -2 = 2 + C ). Solving for ( C ) gives ( C = -4 ). Therefore, the function ( f(x) ) is ( f(x) = (2 - x)e^x - 4 ).

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