# Thread: Limit of defined integral

1. ## Limit of defined integral

$\lim_{n\rightarrow \infty}n\int_{-1}^{0}(x+e^x)^ndx$

The answer it's suppose to be
$
\frac{1}{2}
$

So the value of the integral should be
$
\frac{1}{2n}
$

Direct integration is nonsense.
With First mean value theorem for integration I don't obtain anything.

2. The integral does not need to be 1/ 2n

There are an infinity of possibilites such as 1/2n -e^(-n) for example
though this is not the answer