Find values for real numbers and so that the following improper integral equation holds:

First, we have

In order for this to converge we must have the coefficient of in the numerator equal to 0; hence, we must have . Now, to solve the integral equation we have

But, by assumption this integral equals 1, so we have

Since we then have

I believe that you used the comparison test to state that a=b. If I’m right how can you assure that the analyzed function is >0?

In the second integral, from fifth to sixth row, why did you remove the module? If you keep the module until the end, other solution gonna appear. The other solution is a= -2e-2.