33. Trigonometric improper integrals

▼ IMPORTANT ▼ In this video we will see another solved example of an improper integral from zero to infinity, in this case the quotient (division) of cosine between a sum of squares, and of sine between that sum of squares raised to the square (binomial squared ). For this, we first apply the method of integration by parts, then derivation under the integral sign (Feynman's method or Leibniz's rule), obtaining a relationship between both integrals, and then deriving again, arriving at an ordinary linear second-order differential equation of homogeneous constant coefficients. , which is solved by means of the characteristic equation, arriving at the general solution in terms of a linear combination of exponentials, and finally calculating the value of the constants by evaluating the initial integral at zero, and then at infinity , thus obtaining a pair of initial conditions or boundary values, with which we obtain a 2x2 algebraic system of equations (two equations with two unknowns), which we solve and thus finally obtaining the result. Everything explained step by step.
#feynman #leibniz #integrales
----------
** IMPORTANT LINKS **
Special Videos: • Members-only videos
Mathematics Review Course (Pre-University) • Curso de Matemáticas
----------
** SEE ALL MY COURSES HERE **
/ arquimedes1075
----------
** BIBLIOGRAPHY **
Simplified Mathematics, by Conamat
----------
** DONATIONS **
Paypal: www.paypal.com...
Channel memberships: / @matefacilyt
Patreon: / matefacil
----------
** MY OTHER CHANNELS AND SOCIAL NETWORKS **
Physics Channel: / @matefacilfisica
Videogame Channel: / @matefacily
Twitch: / matefacil
MateFacil App: educup.io/apps...
Facebook (Page): / arquimedes1075
Twitter: @Matefacilx
Instagram: @Matefacilx
Discord: / discord
----------
#Matefacil #Matematicas #Math #tutorial #tutor #tutoriales #profesor
----

[@heliyisraelaguileracalzada6089]

Tengo una duda como sabes que variable tomar al aplicar el truco de feynman?

[@estebanvanegasramos]

Hermosa integral.

[@matematicasconjosue]

Pueden a y b ser negativos??

[@fdelatorre6360]

el curso de fisica preuniversitaria para cuando matefacil 😭

[@carlosespitia5373]

Hola buenos días te saludo desde Colombia. Te quería preguntar porque C1=0 en el límite calculado. Te lo agrradezco

[@ledesmaapariciodaniel6789]

Me hablas del gran Richard P. Feyman?

[@estebanfeliperojasnunez9883]

¿En que curso se ve derivación bajo signo integral?

[@MateFacilYT]

Eso depende de la Universidad y de la carrera que estés estudiando. No siempre es un tema que se vea. Corresponde a un curso de cálculo avanzado o matemáticas avanzadas.

[@estebanfeliperojasnunez9883]

@@MateFacilYT aún no lo es visto en ningún curso pero ahorita que estoy estudiando estadística veo que el libro usa lo de derivación bajo signo integral para una demostración. Menos mal ya vi tus videos 👍🏻

[@faher2012]

La integral cuaticaaaaa! Jskajssj 😯

[@Santi-us8fd]

Gran desvergue😎🤣🤣