Question

(8 pts.) 2. Use the Dise Method to find the volume of the solid formed by revolving the region bounded by the graphs of y = -x + 6x, y-0. and X-0 about the x-axis. 3. Use the Shell Method to find the volume of the solid formed by revolving the region bounded by the graphs of y = x + 4, y = 0, -0. and x - 2 about the y-axis. (8 pts.)

Answer 1

2 y = –??+6ic, y=0 and xao about taxis Disk Method 14 Hi 20 Ya ax²76x Roner radics to outer o adics - x²660 Intersection poonts »x -y o=x²468 O = X(6-2) 03x56 reso, 6 Volume of solid about x-axis b VAST Couter sradics) ?-Pomer radics)9dx asasb OLHSG volumeco)= ((_x44625°-o) dx SC" +363281233 ]dx A T 3 +36 3 xa18 a 4 4 (2=ant n-f1 ET [co (6)5 5 +12 (6) 3 (6)9) o V 2 T 7776 + 129.60-19440 Volámecula 1296 T 5

3 y=x+4, y=0; x 20 and x=2 about y-anis •Y=274 Shell method y mo 202 Radius (R) = x height (h) = (x²+4)0 height-(h) = x²+4 Doo (28) volume of solid about y-anis Y=0x b -San Radius scheight) da a asasb osaca volumec) = (R**** texunds 220. fx carulda. - 21 a 3 BE tua) di =au xe 4 2 care Sana 2021 sti 2 4 + 4x 200 - 27 [ 204 4 + 2x2 221 [ 224 #26232) - ] V = 20 [ Le K f 8 2T (12) = QUI Volume (V.) = 24 TT