Question

计算不定积分∫√9-x²dx

Answer 1

问：计算不定积分∫√9-x²dx

答：亲,您好。计算不定积分∫√9-x²dx∫ √(9 - x²) dx--> x = 3 siny,dx = 3 cosy dy -->= ∫ √(9 - 9sin²y) 3cosy dy= ∫ 3cosy 3cosy dy= 9∫ cos²y dy= (9/2)∫ (1 + cos2y) dy= (9/2)[y + (1/2)sin2y] + C= (9/2)y + (9/2)sinycosy + C= (9/2)arcsin(x/3) + (9/2)(x/3)[√(9 - x²)/3] + C= (9/2)arcsin(x/3) + (1/2)x√(9 - x²) + C