Assignment:
Q1. R is the region bounded by the curve y = x^2 -2x and the x axis. Sketch the given region R and then find its area.
Q2. Using the following integral and the facts that v(t) = x'(t) at time t of an object moving along the x axis is given, along with the initial position x(0) of the object. Answer the questions a - c.
x'(t) = 3(5-2t)^3 ; x(0)=5
a) The position x(t) at time t?
b) The position of the object at time t = 4?
c) The time when the object is at x = 3? Hint: (-3/8(5-2t)^4 +239.3 =3)
Provide complete and step by step solution for the question and show calculations and use formulas.