8 to 10 homework

Find the particular solution of the differential equation that satisfies the initial condition. f' ( x) - 8x, f(0) = 1 f ( x ) Submit Answer 9. [-/10 Points] DETAILS LARCALC11 4.2.064. Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the function and the x-axis over the given interval. f(x) = x2 + 4x, [0, 4] Submit Answer 10. [-/10 Points] DETAILS LARCALC11 4.1.065.MI. Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x'(t) is its velocity, and x"(t) is its acceleration. x(t) = t3 - 12+2 + 21t -9, Osts 10 (a) Find the velocity and acceleration of the particle. x' (t) = x" (t) = (b) Find the open t-intervals on which the particle is moving to the right. (Enter your answer using interval notation.) (c) Find the velocity of the particle when the acceleration is 0