Question

3. Sketch the solid and a typical disk for the solid obtained by rotating the region bounded by the given curves about the specified line. Set up and evaluate an integral that calculates the volume of the solid points) y = **. y = 4, and x = 0 about the y-axis solid and disk: b. Same region as in part (a), about the line y = 4 solid and disk: 4. Find the volume of the tetrahedron using an integral. (3 points) 7 12

Answer 1

The volume of the generated by the curve y=fony about x - aris is b v= it [Rus]" doc. Given that y = 1 + x4 , Y = 4 and x = 0 Ay=x4 - (+424. Disk method: solid a ex&b revolving Region from the region Rly)= 4 y = 1 : x4 4 4 x=0 72 T ac = 1/4 we have Y = 1 / 4 x4 Disk radius is (44) The limits of integration are os yeu By Dilstc methods The volume of given solid, revolusi living is about y-axis V = 1 V- I r [ty lady no roghday CSScanned with CamScanner 4

v = 256 π .: V- 16 IT Î g's dy och da oc ntl noti ta 4 16T 3/2 g 32 T x 8 3/20) (454 ) = 327 3 2 3 16T = X 3 3 CScanned with CamScanner

about the line Pevolving We have y = 1 x" and y=4 y = 4 FY 4 4 solve these two Curves x = | (५ 4 4 20 16 x4 = 24 x = 2 - су, From the region, Disk radius Rool Le- I The limits of integration os asz By Disk method, the volume of solid revolving about the y=4 is CScanned with cathScanner

V (4, da [: (0 - 67 - a4 b - zaby (+ ) a due ㅠ - ) 이 2 S I da ㅠ S 164 ㅗ - 2x4) [Jara nda nf 76 = 1 호 to nti 7 X 2 = ㅠ (bx + 76 9 () (ext 100 피로 ㅠ (2) + 2 (2) 76 ) a 2 2 5 TO i44 2. 은 (2)5) 북 2.5 - 244) 5 32 ㅠ 5 vity + 5 16 -2 144 5144 인 32 720 + 80 - 288 720 572 1 32 TT 720 V 1024T 4 5 잇 ㅠ 51르 45 CSScanned with CamScanner