1. Consider the following indefinite integral: 1 dx cos2 Calculate this integral in two different ways: a. By guessing and checking the antiderivative. b. By using u-substitution. 2. Compute each of the following indefinite integrals: a. Sx2 v2 - 3xdx -dx b. J AtVX S- x 4 V1-xio dx d. ( cosh (x) ax Vx2-1 e. x+1 Vitri ax f. S- tan(nx) COS(TX) g. SVx(2 - x)2 dx 3. Suppose an object moves along an axis, with velocity (in meters per second) given by the following function: pt v(t) = 1 + e2t Assuming the object is positioned at the origin when t = 0: a. What is the position of the object when t = 2? b. What is the change in position of the object over the time interval t E [1, 2]? 4. Suppose an object moves along an axis, with acceleration (in meters per second squared) given by the following function: a(t) = sin (2) Assuming the initial velocity of the object is 1 meter per second, find the change in position of this object over the time interval t E [0, it]