Consider the function given by f(x) = 4x# + 6x3 -30x2 - 64x - 24 that you analysed in Task 1.1. 2.1 Using the answers to Task 1.1, obtain the area enclosed by the curve y = f(x), the x and y-axes and the line x = a, where x = a is the positive root of f(x). 2.2 Obtain the rate of change of f(x) at x = a. The root mean square value of a current i(t) (in mA) between times t = a and t = b (in seconds) is given by iRMS = 2.3 Use a suitable double angle formula to obtain a simplified expression for [i(t)] , where the current i(t) = 9sin(4t + 0.6). 2.4 Obtain the root mean square value (in mA) of the current i(t) = 9sin(4t + 0.6) between times t = 1 and t = 5. The horizontal displacement (in centimetres) of an object from a fixed point, at time t 2 0 (in seconds), is given by s =20cos(2t) + 9sin(4t) + 20e-. 2.5 Obtain the initial horizontal displacement, velocity and acceleration of the object. Interpret what these values mean in terms of the motion of the object. Give your answers in suitable units