Question

Consider the region in the first quadrant bounded by the curves y = 3x, y = 3 - (x - 1)2, and y = 2. (a) Sketch the region. Note all points of intersection. (You may use GeoGebra if necessary, but you can probably do it faster by hand.) (b) Using either the washer or shell method, set up (but do not solve) an integral that computes the volume obtained when the region is revolved about the x axis. Explain why you chose the method you used. (c) Repeat part (b), if the region is revolved about the y axis.

both parts please

Answer 1

* Given curves bei y = 3a.y=3-(2-15h and y-2 A(0,239,3) A(0,2 ya 2 0,223 1 =3-(aa12 Thus the region be AtEA ADDCA The Point of intersection bei Aco, 2); D (1, 2) B (2,27 And C (1,3) using washer method da arus to find the volume about V= n5 [(3x)² = {3-(2-13 23²] an We use about washen method because na anis. the volural is revolved

now when the nesion is revolued about saarisa = M } {%) ² (03-5ad) 2] ay