High score reward! ! ! ! Please help me solve two college physics problems. Please help me.

Have you ever studied advanced mathematics? . .

1. When descending to a height h, superimpose the vertical velocity change during this period with the initial velocity vector, and then superimpose the relative velocity with the implicated velocity (slope velocity) vector

2. This moment of inertia is very basic. . .

3. (1) Find the definite integral. . .

(2) Using the above answer, the kinetic energy theorem comes out.

(3) Yes. According to the loop theorem (the chapter on curve integrals), it satisfies the conservative force condition.