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BC 2,3 Quiz on Chapter 8 Name: __________________ 1.(AP 2008) Let R be the region bounded by the graphs of y sin( x) and y x3 4 x as shown in the figure above. (a) Find the area of R. (b) The horizontal line y 2 splits the region R into two parts. Write, but do not evaluate, an integral expression for the area of the part of R that is below this horizontal line. (c) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a square. Find the volume of this solid. (d) The region R models the surface of a small pond. At all points in R at a distance x from the y-axis, the depth of the water is given by h( x) 3 x . Find the volume of water in the pond. 2. Consider the region R bounded by the graphs of x2 y , y 6 x and y = 0, as shown in the 2 figure at the right. Set up the integral(s), but DO NOT integrate, to find the volume of the solids formed by revolving region R around each of the given axes using the indicated methods. (2, 2) y x2 2 i. x-axis; Washers/Disks ii. x-axis; Shells iii. y-axis; Washers/Disks iv. y-axis; Shells v. y 2; any method vi. x 2; any method vii. Write an integral expression that gives the perimeter of R. y 6 x Extra Credit: Find the area of the region in the xy-plane satisfying x6 x 2 y 2 0