The #1 Calculus Trick You Need to Know BETA GAMMA Relation Simplified

#calculus #iitjee #BetaGammaRelation #jeeadvancedmaths #betafunction #gammafunction #definiteintegral #specialfunctions #csirnetmaths #improperintegrals #polarcoordinates #iitianexplains #gatemaths #mathsolympiad #MATHS&SCIENCE BY IITIAN In this video beta gamma function relation proved B(x,y)= Γ(x)Γ(y)/ Γ(x+y). For knowing the #1 Calculus Trick You Need to Know so that BETA GAMMA Relation Simplified, you are at the right palce. Welcome to the definitive proof of one of the most elegant relationships in advanced calculus: The Beta-Gamma Function Identity — B(x,y)= Γ(x)Γ(y)/ Γ(x+y) In this video, an IITian educator walks you through a step-by-step derivation of this fundamental result—starting from the definitions of the Gamma and Beta functions, using double integrals, and applying a powerful change of variables from Cartesian to polar-like coordinates (via u=st,v=s(1−t) ) with full Jacobian analysis. ✅ What You’ll Learn: Precise definitions of the Gamma function Γ(x) and B(x,y). How to express Γ(x)Γ(y) as a double integral over the first quadrant The change of variables technique that transforms Cartesian coordinates into a product of radial and angular-like components Full computation of the Jacobian determinant Clean separation of integrals to reveal Γ(x+y)⋅B(x,y) Final algebraic rearrangement to prove the identity 🎯 Why This Matters: This identity is not just beautiful—it’s essential for: IIT JEE Advanced (Integral Calculus & Special Functions) IIT JAM Mathematics (Real Analysis & Multivariable Calculus) CSIR-NET Mathematical Sciences (Special Functions & Integral Transforms) MSc/PhD entrance exams and math olympiad-level problem solving Whether you're preparing for competitive exams or simply passionate about deep, conceptual mathematics, this proof will strengthen your intuition for improper integrals, coordinate transformations, and special functions. 🔔 Subscribe for More IIT-Level Mathematics If you're serious about JEE Advanced, IIT JAM, or CSIR-NET, hit Subscribe and turn on notifications! We break down complex proofs, tricky integrals, and exam-critical concepts with clarity, rigor, and IITian insight. 👍 Like if this helped you understand the Beta-Gamma connection! 💬 Comment below: “Gamma-Beta!” if you want a follow-up on applications in probability (Beta/Gamma distributions) or Euler’s reflection formula! The playlist link for all videos is given as below : MATHEMATICS BY IITIAN    • MATHEMATICS BY  IITIAN   Channel Name : MATHS&SCIENCE BY IITIAN Handle : @mathsciencebyiitian Email : [email protected] Kindly view, review and comment on videos for improvement and subscribe to my channel.