Comparison Test for Improper Integrals

The comparison test lets us deduce the convergence or divergence of some improper integrals by relating a complicated function that is challenging to a simpler one we can do. If we compare two functions f(x) greater than g(x) greater than 0, we can deduce things about the convergence of the improper integrals. If the larger integral converges from 1 to infinity, then the smaller one must as well. Likewise, if the smaller one diverges, then the bigger one diverges. We specifically focus on integrals of 1/x^p, which we know precisely when it converges and diverges. Then if there is a more complicated rational function, we can compare it to this. ►Full Course Playlist: CALCULUS II:    • Calculus II (Integration Methods, Series, ...   ♡♡♡SUPPORT THE CHANNEL♡♡♡ ►Support on PATREON:   / drtrefor   ►MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett ►CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes COURSE PLAYLISTS: ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...   ►CALCULUS II:    • Calculus II (Integration Methods, Series, ...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus (Vect...   ►VECTOR CALCULUS (Calc IV):    • Calculus IV: Vector Calculus (Line Integra...   ►DIFFERENTIAL EQUATIONS:    • Ordinary Differential Equations (ODEs)   ►LAPLACE TRANSFORM:    • Laplace Transforms and Solving ODEs   ►GAME THEORY:    • Game Theory   OTHER PLAYLISTS: ►Cool Math Series:    • Cool Math Series   ►Learning Math Series:    • 5 Tips To Make Math Practice Problems Actu...   ►LaTeX:    • Intro to LaTeX **Full Tutorial**  Part II ...   SOCIALS: ►X/Twitter: http://X.com/treforbazett ►TikTok:   / drtrefor   ►Instagram (photography based):   / treforphotography