① The integral curve is a star line, and the parameter equation of the star line is x = a (cost) 3, y = a (Sint) 3, 0≤t≤2п.

② Substitute into the simplified integrand function:

x^(4/3)+y^(4/3)= a^(4/3)[(cost)^4+(sint)^4]，

Use trigonometric formula (cost) 2 = 0.5 (1+cos2t) 2, (Sint) 2 = 0.5 (1-cos2t) 2 ★ to reduce the order and then reduce it.

Integrative function = 0.5a (4/3) * [1+(cos2t) 2].

③ find ds:

Same as above, by simplifying the formula★, we can get DS = √ (x') 2+(y') 2dt =1.5a ┃ sin2t ┃ dt.

④ Calculate the original formula:

∫ x (4/3)+y (4/3) ds = 0.75a (7/3) ∫ (0 to 2 п) [1+(cos2t) 2] * ┃ sin2t ┃.

Considering the sign of ┃sin2t┃ in the integrand function between 0 and 2п, when removing the absolute sign,

The integration interval needs to be divided into four sections: 0 to п/2, п/2 to п; п to 3 п/2; 3п/2 to 2п,

Then the original formula = 4a (7/3) can be obtained by integrating one by one.