1 / | | 2 | x | -- | 2 | x*e dx | / 0
Integral(x*exp(x^2/2), (x, 0, 1))
There are multiple ways to do this integral.
Let .
Then let and substitute :
The integral of a constant is the constant times the variable of integration:
Now substitute back in:
Let .
Then let and substitute :
The integral of the exponential function is itself.
Now substitute back in:
Now simplify:
Add the constant of integration:
The answer is:
/ | | 2 2 | x x | -- -- | 2 2 | x*e dx = C + e | /
1/2 -1 + e
=
1/2 -1 + e
-1 + exp(1/2)
Use the examples entering the upper and lower limits of integration.