NAME: ID#: ISC 101B Calculus II Summer 2016 W. Smith Worksheet 1, due Thursday June 30 1. Evaluate the definite integrals: Z 3 5 a. (2x2 12x + 13 3 )dx x 1 2 Z b. 3 cos(2x)dx 6 Z 3 1 4(2x + 3) 3 dx c. 1 2. Find F 0 (x) for each problem: Z x a. F (x) = (3y 2 + y 7)8 dy 3 Z b. F (x) = 5 3. x4 1 dt t5 Find the area of the region with 0 x that is above the graph y = 1 + cos x and below the line y = 2. 4. 5. 3 Find the area of the region between the curves y = 2 x2 and y = x. Use the disk method to find the volume of the solid that results when the region enclosed by the curves y = 2x + 2, y = x2 + 2 is revolved around the x-axis. 6. Use the shell method to find the volume of the solid that results when the region enclosed by the curves is revolved around the given axis: a. y = 2x, y = x/2, x = 1; axis the y-axis. b. x = 2y y 2 , x = y; axis the x-axis