求教高数题 详细过程 谢谢🙏

Question

画圈的第三大题第1题 第2题 详细过程解答谢谢🙏

Answer 1

分部积分法追问

我知道啊😂 是想看看详细过程

Answer 2

令 (3-2x)^(1/3) = u,  则 3-2x = u^3,   x = (3-u^3)/2,   dx = (-3/2)u^2du

I = (-3/4)∫(3-u^3)u^2du/u = (-3/4)∫(3u-u^4)du

= (-3/4)(3u^2/2 - u^5/5) + C = (-3/4)u^2(3/2 - u^3/5) + C

= (-3/40)(9+4x)(3-2x)^(2/3) + C

令 x = sinu, 则 dx = cosudu

I = 2∫<0, 1/2> xarcsinxdx/√(1-x^2) = 2∫<0, π/6> usinucosudu/cosu

= 2∫<0, π/6> usinudu = -2∫<0, π/6> udcosu


= -2[ucosu]<0, π/6> + 2∫<0, π/6> cosudu

= -√3π/6 +  2[sinu]<0, π/6> = 1-√3π/6

Answer 3

不懂找百度

Answer 4

如图所示。

本回答被提问者采纳

Answer 5

2分之一，