Question

微积分求解：∫根号下(4-x^2) dx 谢谢。

微积分求解：∫根号下(4-x^2) dx

积分号上面是2，下面是0。谢谢。
晕，好歹给个思路阿。。。我又不是只要答案。
2楼的没看见根号阿。

Answer 1

令x=2siny,则y在0到pi/2之间
∫根号下(4-x^2) dx *******[0，2]
=∫根号下（4-4sin^2y)d(2siny) *******[0,pi/2]
=∫4cosyd(siny)*******[0,pi/2]
=∫4cos^2ydy*******[0,pi/2]
=∫2[1+cos(2y)]dy*******[0,pi/2]
=∫2[1+cos(2y)]dy*******[0,pi/2]
=[2y|0,pi/2]+[sin(2y)|0,pi/2]
=pi

Answer 2

∫(4-x^2) dx =4x-x^3/3
所以原式＝2(4x-x^3/3)=8-6/3=18/3

Answer 3

设 x=2siny.. 后面自己做

Answer 4

令x = 2sinθ、dx = 2cosθ dθ
∫(0→2) √(4 - x?) dx
= ∫(0→π/2) 4cos?θ dθ
= 2∫(0→π/2) (1 + cos2θ) dθ
= 2[ θ + (1/2)sin(2θ) ]：(0→π/2)
= 2[ π/2 + 0 ]
= π

Answer 5

=16/3