求积分 ∫1到8 [(x^1/3+1)(2-x^2/3)]/x^1/3 dx

求积分 ∫1到8 [(x^1/3+1)(2-x^2/3)]/x^1/3 dx
求积分 ∫1到8 [(x^1/3+1)(2-x^2/3)]/x^1/3 dx

求积分 ∫1到8 [(x^1/3+1)(2-x^2/3)]/x^1/3 dx
=∫[x^(1/3)-x+2-x^(2/3)]/x^(1/3)]dx
=∫[1-x^(2/3)+2x^(-1/3)-x^(1/3)]]dx
幂函数积分
=x-x^(5/3)/(5/3)+2x^(2/3)/(2/3)-x^(4/3)/(4/3)(1,8)
代入算一下吧

原来每个表面积是2×(15×8+15×4+8×4)=424
现在减少了两个面
所以有三种情况
2×424-2×15×8=608
2×424-2×15×4=728
2×424-2×8×4=784
答：涂色部分的面积是608平方厘米或728平方厘米或784平方厘米