Fourier Series: Half Range Sine Series of f(x) = lx - x² | Explained

VTU Half Range Fourier Sine Series | f(x) = lx − x² in 0 less than x less than l | 1BMATEE301 Module 2 | 1BMATEC301 Module 1 | 1BMATME301 Module 1 In this video, you'll learn how to show that the sine half range series for the function f(x) = lx − x² in 0 less than x less than l is (8l²/π³) * sum from 0 to infinity of 1/(2n+1)³ * sin((2n+1)πx/l) — an important VTU 3rd Semester exam topic. Step-by-step solution for VTU 2025 Scheme students. ━━━━━━━━━━━━━━━━━━━━━━ APPLICABLE FOR VTU SUBJECT CODES ━━━━━━━━━━━━━━━━━━━━━━ 🔹 1BMATEE301 – Module 2: Fourier Series 🔹 1BMATEC301 – Module 1: Fourier Series 🔹 1BMATME301 – Module 1: Fourier Series ━━━━━━━━━━━━━━━━━━━━━━ SYLLABUS TOPIC ━━━━━━━━━━━━━━━━━━━━━━ Fourier Series – Half Range Fourier Sine and Cosine Series ━━━━━━━━━━━━━━━━━━━━━━ PROBLEM SOLVED IN THIS VIDEO ━━━━━━━━━━━━━━━━━━━━━━ Show that the sine half range series for the function f(x) = lx − x² in 0 less than x less than l is: (8l²/π³) * sum from 0 to infinity of 1/(2n+1)³ * sin((2n+1)πx/l) ━━━━━━━━━━━━━━━━━━━━━━ PREVIOUS VIDEO ━━━━━━━━━━━━━━━━━━━━━━ Half Range Fourier Cosine Series of f(x) = 2x − 1    • Solve f(x) = 2x - 1: Half Range Cosine Ser...   ━━━━━━━━━━━━━━━━━━━━━━ NEXT VIDEO IN THIS SERIES ━━━━━━━━━━━━━━━━━━━━━━ Show that l/2 − x = (l/π) * sum from n=1 to infinity of 1/n * sin(2nπx/l), 0 less than x less than l    • Can You Solve This? | Half Range Fourier S...   ━━━━━━━━━━━━━━━━━━━━━━ COMPLETE PLAYLISTS BY SUBJECT CODE ━━━━━━━━━━━━━━━━━━━━━━ 🔹 1BMATEE301: ▶️ Module 1 – Complex Analysis    • 1BMATEE301 Module 1 | Complex Analysis Pro...   ▶️ Module 2 – Fourier Series    • 1BMATEE301 Module 2 | Fourier Series Compl...   ▶️ Module 3 – Fourier Transforms & Z-Transforms    • 1BMATEE301 Module 3 | Fourier Transforms &...   ▶️ Module 4 – Probability Distributions & Sampling Theory    • 1BMATEE301 Module 4 | Probability distribu...   ▶️ Module 5 – Linear Programming Problems    • 1BMATEE301 Module 5 | Linear Programming P...   ━━━━━━━━━━━━━━━━━━━━━━ 🔹 1BMATEC301: ▶️ Module 1 – Fourier Series    • 1BMATEC301 Module 1 | Fourier Series Compl...   ▶️ Module 2 – Fourier Transforms    • 1BMATEC301 Module 2 | Fourier Transforms C...   ▶️ Module 3 – Z-Transforms    • 1BMATEC301 Module 3 | Z-Transforms Complet...   ▶️ Module 4 – Linear Programming Problems    • 1BMATEC301 Module 4 | Linear Programming P...   ━━━━━━━━━━━━━━━━━━━━━━ 🔹 1BMATME301: ▶️ Module 1 – Fourier Series    • 1BMATME301 Module 1 | Fourier Series Compl...   ▶️ Module 2 – Fourier Transform & Z-Transform    • 1BMATME301 Module 2 | Fourier Transform & ...   ▶️ Module 3 – Partial Differential Equations    • 1BMATME301 Module 3 | Partial Differential...   ▶️ Module 5 – Statistics-2    • 1BMATME301 Module 5 | Statistics-2 Complet...   ━━━━━━━━━━━━━━━━━━━━━━ WHO IS THIS FOR? ━━━━━━━━━━━━━━━━━━━━━━ BE/B.Tech 3rd Semester VTU & Autonomous students (Karnataka) Subject Codes: 1BMATEE301, 1BMATEC301, 1BMATME301 Branch: EEE, ECE, Mechanical and allied branches For Autonomous colleges – if you have this in your syllabus, study this Students preparing for VTU internals, externals & backlog exams ━━━━━━━━━━━━━━━━━━━━━━ WHY WATCH THIS VIDEO? ━━━━━━━━━━━━━━━━━━━━━━ Step-by-step VTU exam solution Exam-focused VTU & Autonomous problems Simple, easy-to-understand method Covers repeated VTU exam questions Perfect for last-minute VTU revision ━━━━━━━━━━━━━━━━━━━━━━ STAY CONNECTED ━━━━━━━━━━━━━━━━━━━━━━ 💬 WhatsApp Channel: https://whatsapp.com/channel/0029Vb6c... 📩 Telegram: https://t.me/vtumathswithmathematicst... 📸 Instagram: https://www.instagram.com/_mathematic... Subscribe & hit the bell icon so you never miss a video! If this video helped you, LIKE, SHARE with your VTU classmates, and COMMENT which problem you want next! #VTU #VTUKarnataka #1BMATEE301 #1BMATEC301 #1BMATME301 #FourierSeries #HalfRangeSeries #EngineeringMathematics #VTU2025 #VTU3rdSem #VTUMaths #VTU2025Scheme #VTUExams #VTUImportantQuestions #EEE #ECE #Mechanical #BETech #Autonomous