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MAC 2312 Exam 2 Spring 2011 Key

# MAC 2312 Exam 2 Spring 2011 Key - MAC 2372 EXAM K 2 SpnrNc...

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MAC 2372 Name K ey EXAM 2 SpnrNc 2011 \$d.t # zc SHO\M ALL WORK TO RECEIVE FULL CREDIT. Jl'- 1. Take the region bounded by A : 12 and n : A2 and set up the integral for determining the volume when you rotate the region about line g - -1. Use the Shell method. DO NOT EVALUATE THE INTEGRAL. The shrl,[ hCIs hndius J *l , J J v:X 7T,trfl) {.,S ,*lz tl 3F "rrd the volume of the solid obtained by rotating the region bounded by a2:t ancl Svt r :2y about the y-axis. Use the washer method. Also sketch the region being rotated. CiWurr,fpiic& 27[ rJ+r ), e*,'d hr\$t't ^ff - y'= A ckoss4ec+tbn is a washeY W(+h inr-tlt fadiqs U' and gu-te,v ra ltus Lg , .(o lts area is AtY) = r, (zY)' -7r U)' -- n&f- rr, @ 5o. v = J^ At,l,dv = n l,' (+v'- Yr) 6- :7r€y'-+J')l: :r,({ -?) =#n {1 dj Jt/" ,l V= {' )0 6 @

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[6,V *to 3. If the work required to stretch a spring 1 ft beyond its natural length is 12 ft-lb, then ' u) what is the spring constant according to Hooke's Law? zvs n=l,krdY=+kx'lj =+* =+ k=21 tLftt zve b) How much work is needed to stretch it 9in. beyond it's naturai length?
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MAC 2312 Exam 2 Spring 2011 Key - MAC 2372 EXAM K 2 SpnrNc...

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