3. (12%) Evaluate ∫_0^1 x √1-x^3 dx

8. (13%) Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, u(1, 2) = 5, $u_0(1, 2) = 4$, $u_0(1, 2) = -3$, v(1, 2) = 7, $v_0(1, 2) = 2$, $v_1(1, 2) = 6$, $G_u(5, 7) = 9$, $G_v(5, 7) = -2$. Find $R_0(1, 2)$ and $R_1(1, 2)$.