20E_Exam2A_soln

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A MATH 110 EXAM #2 Please answer the following questions. You will not get credit for answers un- Iess you demonstrate how you arrived at them. In short, please show all work' Numerical integrations by calculator will not be accepted. PRoBr,pufl(30ets.) Consider the region in the plane R: {l ( y ( 2, -y ( r ( y} (see the picture below). Use the change of variables t :'u1)t A : u to compute the integral: r - tt (\4ff dxd,y . J Jn Yu/ (Hint: One of the main things you need to figure out is the limits of integration in the (u, u) coordinates). U=& 3=l Lu,r\JS irr {-r,** g;d b us \rt , {:gf L4 !1 t t*\ \$ rt r'4 s ' *s' I*) | S Ir Vericz L"Lt' 't V {) t ? ? 1 E** Z* I I I LL \r .---*') tl-/e't I N( r(bure ; *i--: ag]i {-g **L; E' ,_l *-".*.4 lhc d* Lr u*_ I \$ ! 7 4 rfu t.,( f: .ry \T v {-l\<;1n3* fyrin,*'/'b , 2* 1Z Lv fr dl \r s ,' Thq /*., \*.- l ^,

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I a\ PRoelpu #2 (40 em. totel) Consider the vector-field F : (r2,*g) in the plane. Please ansvrer the following: a) (15 pts.) Compute the line integral t F.A of F over the parameterized curve c-1(t) : (cos(t),2sin(t)) between 0 < < zr (see the direction of dr in the figure above). d; [\$ 'i [-shbre(*tt] {' '-'"\ il \ r- i, ij l h*' &'
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