MTH 133 Quiz: MTH133 Quiz 2 2017 Spring Version A Solutions

1. 0/10 points | Previous Answers a. Calculate the volume of the solid of revolution created by rotating the curve about the x-axis, for x between 3 and 4 Volume XYour answer cannot be understood or graded. More Information b. The equation of a circle of radius r, centered at the origin (0,0), is given by Rearrange this equation to find a formula for y in terms of x and r. (Take the positive root.) Equation: y o What solid of revolution is swept out if this curve is rotated around the x axis, and x is allowed to vary between -rand r? (You do not need to enter this answer into WebAssign.) o Suppose we wanted to set up the following integral so that Vgives the volume of a sphere of radius r V= | f(x) dx What would a, b and f(x) be? rx) = (WebAssign note: remember that you enter π as pi ) o Carry out the integration, and calculate the value of V in terms of r. ymbolic formatting he Submit Answer Save Progress Submit Assignment Save Assignment Progress

MTH 151 - Volumes Using Integrals For each of the following (10 points each) Sketch the graph of the indicated region. The points of intersection of the boundaries of the region are probably self-evident, but pay attention to where they are. (2 points) Expand your graph to show the solid generated by revolving the region about the indicated line. (1 point) Use disks, washers, or shells, as directed, to find an integral for the volume of the solid and include a "sample slab" in your graph. (4 points) Use the first form of the Fundamental Theorem of Calculus to find the volume. Include the antiderivative you use and your substitutions into that antiderivative. (3 points) . o . . 1. The region is bounded by the graphs of y =ç º, x = 1, x = 8, and y = 0, Use disks to 2. The region is bounded by the graphs of y = and y = x2. Use washers to find the 3. The region is bounded by the graphs ofy = find the volume when the region is revolved about the x-axis. volume when the region is revolved about the line y = 1.5 when the region is revolved about the line x =-1. y-x. Use shells to find the volume