e^{-(x² + y²)} | Polar Coordinates Solve What Cartesian Cannot

Learn Gaussian Integrals with an important VTU Integral Calculus problem solved step-by-step. Perfect for understanding multiple integrals involving exponential functions and advanced integration techniques. ━━━━━━━━━━━━━━━━━━━━━ 📘 Subject Mapping: 📚 Integral Calculus & its Applications for: • 1BMATE201 – Module 1 • 1BMATC201 – Module 1 • 1BMATM201 – Module 1 ━━━━━━━━━━━━━━━━━━━━━ 📌 Exact Question (with Timeline): ⏱ 00:00 → Evaluate the double integral ∬ e^{−(x²+y²)} dxdy Limits: x = 0 to ∞ y = 0 to ∞ ━━━━━━━━━━━━━━━━━━━━━ 🎯 Learning Points: ✔ Gaussian Integral step-by-step ✔ Exponential function integration ✔ Infinite limits in double integrals ✔ Polar coordinate transformation ✔ VTU exam solving techniques ✔ Advanced integration simplification methods ━━━━━━━━━━━━━━━━━━━━━ 📚 Watch Next: 1️⃣ Area & Volume Applications    • Expected Questions for Integrals, Areas & ...   2️⃣ Beta Function Identity    • Beta and Gamma Functions Relationship Expl...   3️⃣ Full Integral Calculus Playlist    • 1BMATE201 Module 1 | Double Integrals, Tri...   ━━━━━━━━━━━━━━━━━━━━━ 📘 Module Playlist (Start to Finish): ▶️ 1BMATE201 Module-1: Integral Calculus & its Applications    • 1BMATE201 Module 1 | Double Integrals, Tri...   ━━━━━━━━━━━━━━━━━━━━━ 📙 More Practice / Related Method: 1️⃣ Prove Γ(1/2)=√π    • Proof That Gamma(1/2) = √π | VTU Important...   2️⃣ Beta & Gamma Function Identity    • ∫√sinθ dθ × ∫1/√sinθ dθ = π Proved | Beta ...   ━━━━━━━━━━━━━━━━━━━━━ 🚀 Next Step: Continue with Beta and Gamma Function problems for complete VTU Integral Calculus preparation. 📌 Don’t stop here: Practice Gaussian Integrals and coordinate transformations regularly to improve speed and accuracy in VTU exams. ━━━━━━━━━━━━━━━━━━━━━ 🔥 MOST IMPORTANT PLAYLISTS (Newly Updated) 📘 Numerical Methods 1 VTU Playlist 👉    • Numerical Methods 1 VTU Playlist | Regula ...   ━━━━━━━━━━━━━━━━━━━━━ 📙 Important 1BMATE201 Playlists 📌 Module-1: Integral Calculus 👉    • 1BMATE201 Module 1 | Double Integrals, Tri...   📌 Module-2: Vector Calculus 👉    • Vector Calculus & Applications | VTU 1BMAT...   📌 Module-3: Numerical Methods-1 👉    • 1BMATE201 Module 3 | Numerical Methods I |...   📌 Module-4: Numerical Methods-2 👉    • 1BMATE201 Module 4 | Numerical Methods II ...   📌 Module-5: Laplace Transforms 👉    • 1BMATE201 Module-5: Laplace transforms   ━━━━━━━━━━━━━━━━━━━━━ 👉 Follow VTU Maths with Muheeb (Mathematics Tutor) on WhatsApp https://whatsapp.com/channel/0029Vb6c... 👉 Get all VTU Maths updates and video links on Telegram https://t.me/vtumathswithmathematicst... 💎 Support Us: Join our channel and get access to exclusive perks 👇    / @officialmathematicstutor   ━━━━━━━━━━━━━━━━━━━━━ #GaussianIntegral #IntegralCalculus #DoubleIntegrals #VTUMaths #1BMATE201 #EngineeringMathematics #MathsMadeEasy