Math 1360 Exam 1 Review (Chapter 6-7.5) Name___________________________________ 1) a) Evaluate each of the following: x e dx (Hint: Start with a u- substitution for the square root of x.) /4 b) sec 0 4 x tan 4 xdx x 1 c) x( x 2) d) 2 dx 25 x 2 dx 2) How many midpoint rectangles would you have to use in estimating the area under f(x)=2x between x=0 and x=2 to get your answer accurate within 0.1? Hint: The derivative of bx is (lnb)bx.(Your answer will look messy- that’s OK.) 3) Evaluate the following integrals: 1 a) 2 dx 1 x 1 b) 8 x dx 0 4) Set up, but do not evaluate, an integral to find the following: a) The area of the region in the first quadrant bounded by y=tanx, y=1 and the y-axis. b) The volume that results when the region bounded by y=x and y=x2 is rotated about the line x=4. c) The length of the curve that encloses the region bounded by y=x and y=x2. d) The volume of the solid generated when the region bounded by y=sinx and y=cosx between x=0 and x=π/4 is rotated about the y-axis. e) The volume of the solid generated when the region in the first quadrant that is bounded by x=y2, the y-axis and y=4 is rotated about y=5. f) The volume that results when the region bounded by y= -x2+4 in the first quadrant is rotated about the x-axis. g) The surface area of the solid bounded by y=sinx, x=0, x=π/2 and the x-axis is rotated about the x-axis.