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.