AP CALCULUS BC
Arc Length Geometry
Integration geometric summation modeling arc length via continuous reduction of $ds = \sqrt{dx^2 + dy^2}$ discrete limits approaching exact mathematical integrals. Reveals consistent finite approximation underestimation behavior against true curved lines.
AP CALCULUS BC
Surface Area of Revolution
3D wireframe rendering of surfaces of revolution around the x-axis. Demonstrates S = ∫2πf(x)√(1+f'(x)²)dx with interactive rotation angle and bounds. Explore Sphere, Cone, Gabriel's Horn, and Sine Vase with drag-to-orbit camera.