number 12 part A and B please write/post clearly and post multiple pictures O D.
ID: 2881729 • Letter: N
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number 12 part A and B please write/post clearly and post multiple pictures
O D. dy The area of the surface is (Do not round until the final answer. Then Square units. round to the nearest hundredth as needed.) 12. Find the volumes of the solids generated by revolving the region in the first quadrant bounded by the curve x 9y 9y and the y-axis about the given axes a. The x-axis b. The line y 1 a. The volume is 3 of 7 2/18/2016 2:57 PM https://xlitemprod pearsoncmg.com/api/vilprint/math Test (Chapter 7)(Ron Larson) (Type an exact answer in terms of b. The volume is (Type an exact answer in terms of Find the of surface generated by revolving the curve y 2x x2 0.25 s xs 1.5, about the x-axis. area the The area of the surface generated by revolving the curve y 2x-x2 0.25 sxs 1.5, about the x-axis is square units. (Type an exact answer, using as needed.) 14. Find the volume of the solid generated by revolving The volume of the solid is €ubig dhits the shaded region about the x-axis. (Type an exact answer, using R as neededExplanation / Answer
12 a) we have given x=9y-9y^3 and y-axis means x=0
intersecting point curves 9y-9y^3 =0
y(9-9y^2)=0
y=0,9y^2=9 implies y=1,-1
y bounds are 0 to 1
radius of the disc is r=9-9y^3
The volume about the x-axis is integration of (y=0 to 1) pi*(9y-9y^3)^2dy
integration of (y=0 to 1) pi*(9y-9y^3)^2dy=integration of (y=0 to 1) pi*(81y^2+81y^6-162y^4)dy
=pi*[(81/3)*y^3+(81/7)*y^7-(162/5)*y^5] from y=0 to 1
=pi*[(81/3)+(81/7)-(162/5)]
=pi*[(81*7*5)+(81*3*5)-(162*7*3)]/105
=pi*(648/105)
V=pi*(216/35)
b) we have given x=9y-9y^3 and y-axis means x=0 about the line y=1
radius r=1-y and h=x=9y-9y^3
by using shell method
volume V= integration of (y=0 to 1) 2pi*r*h dy
V= integration of (y=0 to 1) 2pi*(1-y)*(9y-9y^3) dy
=2pi*integration of (y=0 to 1) (9y-9y^3-9y^2+9y^4)dy
=2pi*[(9/2)y^2-(9/4)y^4-(9/3)y^3+(9/5)y^5] from y=0 to 1
=2pi*[(9/2)-(9/4)-(9/3)+(9/5)]
=2pi*[((30*9)-(15*9)-(20*9)+(12*5))/60]
=2pi*[(15)/60]
=12pi/4
V=3pi
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