1. Evaluate each integral by making an appropriate substitution. x (c) Itan x sec4xdx 2. Find the area of the region bounded above by the graph of g(x) = l and below by the graph off(x) 2x2 +2x2. 3. Let R be the closed region between the graphs of y = 2d; and y = 2x on the interval [0, 1]. Find the volume V of the solid obtained by revolving R abont the x- axis. 4. Let R be the closed region between the graphs of y = 2d; and y = 23: on the interval [0, 1]. Find the volume V of the solid obtained by revolving R about the y- axis. (Same graph as for Problem3) 5. Find the length of are on the graph of f(x) 2 2arm 3 from x=1 to x=4 6. Find the area of the surface generated by revolving about the x-axis the curve f(x) = %x3 on [0,2]. 7. Fill in the values of f '10:) and (f '1)'(x) for x = 1, 2, 3. Provide detail to Support your answers. x 1'06) f'Cx) For) (rim) 1 2 5 2 3 l 3 l 3 8. CaICulate the derivative for y = aretan(~v'x2 +1) 9. Use the definition of an improper integral to evaluate the following integrals. If an integral converges, evaluate its value. I 1 (a) [a 9 dx 0. I (b) J-v: 2x Ixz+ldx