00:01
I given i n is equal to integral 0 to n e rise to the power minus s t into e rise to the power 3 t into d t we need to compute this integral this implies i n is given by integral 0 to n e rise to the power 3 minus s into t into d t now integrating with respect to t we have e rise to the par 3 minus s into t divided by the coefficient 3 minus s within the limits 0 to n.
00:49
Therefore, substituting the limit and simplifying finally we get in is equal to e rise to the power 3 minus s into n minus 1 divided by 3 minus s.
01:06
Next, we need to take the limit n tending to infinity to the obtained expression, that is, limit intending to infinity, e rise to the power 3 minus s into n minus 1 divided by 3 minus s.
01:28
This can be written as limit intending to infinity, e rise to the power, s minus 3 minus 3 ,000 into minus 3.
01:38
Minus n minus 1 divided by 3 minus s.
01:46
Now applying the limit we have e rise to the power minus infinity is 0.
01:52
Therefore we have minus 1 divided by 3 minus s.
01:57
This can also be written as 1 divided by s minus 3...