University:
University of Central Florida
Course:
MAC 2312 | Calculus with Analytic Geometry II
Academic year:

2023
Views:

359

Pages:

4
Author:

Maria

3.3. Trigonometric Substitution L Consider √9-x² Let x = 3 sin θ =√9-9sin² = 3√1-sin² = 3√cos² = 31cos 01 ff(g(x)) g'(x) dx = f(u) du let u = g(x) Ex: x2 dx let x = 3 sing dx= 3 cas de 9- =SJg9sin² 3 cos de = 3√1-sin20 3 cos de I sin 2 9 sin cos df = COS 2 Scat de sin Ngoài lề: 1 + cot² 0 = csc =) ext² = csc 20-1 = Sese² I decat - We know: x = 3 sin sin We want cort =? Ex: =S2' tan² 1 2' tan √4 tan θ - Sz²'tan (2) √tan'0+1 zsecodo St sec de tan' sec² Let x = 2 tan θ dx = 2 sec² de 2 sec² do 2 2 tan seco 4 cos 2. cose do sin Sainte cos e de u = sin du cos de = Sedu=u+ c = csc O + C 4 4 2 We know tan = 2 We want ese?