This animation walks through solving the integral of x³ sin(x) dx using repeated integration by parts. It shows how to choose u and dv, apply the formula ∫u dv = uv − ∫v du multiple times, and simplify step by step until reaching the final answer: −x³cos(x) + 3x²sin(x) + 6xcos(x) − 6sin(x) + C. Useful for Class 12 students and beginners learning repeated integration by parts techniques.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
Create a step-by-step animated mathematics lesson explaining the integration of x³ sin(x) dx. Audience: Class 12 and beginner calculus students. Format: Vertical 9:16, approximately 30–45 seconds. Visual style: Clean whiteboard, handwritten equations, smooth mathematical animations, clear black text, and subtle blue highlights. Scene 1: Display the question ∫x³ sin(x) dx and ask students to solve it. Scene 2: Introduce the integration by parts formula: ∫u dv = uv − ∫v du. Scene 3: Show u = x³, dv = sin(x) dx, du = 3x² dx, and v = −cos(x). Scene 4: Reveal each substitution and simplification one line at a time. Scene 5: Apply integration by parts to the remaining integral until it is completely solved. Scene 6: Reveal and highlight the final answer: −x³ cos(x) + 3x² sin(x) + 6x cos(x) − 6 sin(x) + C. End with: “Follow for more calculus lessons.” Keep all mathematical expressions accurate, use smooth transitions, and avoid overcrowding the screen. Show one equation at a time.