00:01
Consider the improper integral from negative infinity to infinity of 2x over the square of x squared plus 1 dx.
00:08
In here we will express the improper integral as a limit of definite integrals, then we will evaluate it.
00:15
For the first part, by definition, the integral from negative infinity to infinity of 2x over the square of x squared plus 1, dx is equivalent to the integral from negative infinity to a real number c let's say c is zero know that we can choose any real number as long as it makes the integran defined and then we have 2x over the square of x squared plus 1 d x this plus the integral from 0 to infinity of 2x over over the square of x squared plus 1, and then dx.
01:01
And then by definition again, this is equal to the limit as a approaches negative infinity of the integral from a to 0 of 2x over the square of x squared plus 1, dx, plus you have the limit as b approaches infinity of the integral from 0 to b of 2x over the square of x squared plus 1, and then d x.
01:26
Next for part b, we will evaluate what we have in part a.
01:30
Now, to evaluate, first want to do substitution...