How do you find the definite integral for: e^(5x) dx for the intervals [0, 1]?
1 Answer
Explanation:
We want to find:
int_0^1e^(5x)dx
Our goal for integration should be to get this integral into the pattern:
inte^udu=e^u+C
Thus, we substitute and let
To have our
=1/5int_0^1e^(5x)*5dx
We now see that this will fit the
Do this by plugging the current bounds of
u(0)=5(0)=0
u(1)=5(1)=5
Thus,
1/5int_0^1e^(5x)*5dx=1/5int_0^5e^udu
We can now evaluate the integral from
=1/5(e^u)]_0^5=1/5(e^5-e^0)=(e^5-1)/5