∫ √(1−x²) dx integrieren – Trig. Substitution, Verifikation & Fläche | Mathefrosch

Together we calculate the integral of √(1−x²) dx – using trigonometric substitution (x = sin θ) and the half-angle for cos²θ. Result: ½·(x·√(1−x²) + arcsin x) + C. Verifying this by differentiation (product rule) and the definite integral from 0 to 1, we find the area of ​​the quarter circle π/4 ≈ 0.785. Chapter: 0:00 Intro 1:18 Integration – Trigonometric Substitution 4:03 Verification 4:51 Area The Math Frog shows you how it's done step by step. Subscribe for more integral calculus! #mathfrog #integralcalculus #integrate #analysis #substitution #trigonometry #arcsin #antiderivative #math #mathematics