Improper integral solved with the residue method
How to solve a definite (improper) integral using the residue method .
After having discussed the residue method , we take the opportunity to solve an improper integral for which integrand function is complicated to find a primitive using elementary integration methods .
After having demonstrated that the improper integral exists finite (integrability criteria) we will extend the integrand function to a complex function of complex variable and in the Gaussian plane we will determine a generally regular curve in order to apply the residue theorem .
Here are some preparatory lessons to better understand this lesson:
Integrability criterion in the case of a limited domain, but with an "infinity" point
• Integrali impropri o generalizzati su inte...
Integrability criterion in the case of an unlimited integration domain
• Integrali impropri su intervalli illimitat...
Logarithm in the field of complex numbers and "cut plane"
• Il logaritmo nel campo complesso .
Isolated singular points
• Punti singolari : polo , singolarità fitti...
Residue method
• Integrali con il teorema dei residui .
#salvoromeo #metododeiresidui