midterm1+solutions

midterm1+solutions - t(10points ifpossible Evaluate a...

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t. (10 points) Evaluate ifpossible. a) Jcos'(nr)sin(ru)at lvt t' : \t^ : l,c" Co; fi4 dw= -bin TTt. ff dt b't'A f L d+ oJnL+c a 1f r1-4r \ ff) , ,.* I TTtc=-ffi Cher-k.: L dt, : ( ft o* tr+ + c-) - # ,f ,oJ Tft.( cp'?rL ';in f L 9in 1II).7 +6 b) i .P- *'\^tu 'o ' lor wa q'x7 dw= - >xd\ xdt<, + ,u;h+-* X= O,lL=1 vche* X=b ,l-L-- 4-V>= 0 o ( .* r dt = J a'[- 3) qA :-i+1: '(Dh-qo) 'qb : 1- ,lD

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(10 points) Find the number b such that the line y = b divides the region bounded by the curves ! : x2 and y = 4 (as shown) into tvro regions with equal area. 5"+ j=*-, K= ! {t :>, + A^a , &vtr # %4^ @ '- &naa oP re1,ro"@ , ,V12. + ,oln ?b 7 30 . rvl> D= )\=f"rg d5 o : ,:t11o = T'), A"u, o\$ gon @ ,Jf ory - ( rr))db= 4/,71> */r .. hb -=./e(4 ?l)- ll> vd r+ f'' r 8'n, 7t> _ j,-) IJ,, al> >D: tlv Ll >l> 4 T f,qr, 'o*#Jro \(r'''-f") zlt
3. (10 points) Determine the volume of the sotid obtained by rotating the region bounded by ! = x3, ) 8o and .r =0 (as shown) aboutthe line x =2. a .'. . V=JntSlar xc L0aav,u Gvt A(5) n z> j''''r G''' (.""?- r,^ I ./ !=( ) o ?t) n( I Cn '-7 Gvf ii (u {'t - f'-) al t ,+b ,bl) 18 :n(+ *- +)l "nl, 4b , )u r 4 .{lt- 7 A"t+-o) =fi [+ q'6

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This note was uploaded on 04/25/2008 for the course MATH 2B taught by Professor Staff during the Winter '05 term at UC Irvine.

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midterm1+solutions - t(10points ifpossible Evaluate a...

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