MAC 2312 Exam 1 Spring 2011 Key

# MAC 2312 Exam 1 Spring 2011 Key - MAC 2312 Tpsr I Srnrxc...

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MAC 2312 Tpsr I Srnrxc 2011. Name kEY Lt^+z . Tl"0 soV"+ion iJ ho* u'i?tro' IYU N . ' SHOW ALL WORK TO RECETVE FULL CREDIT. Each question is worth 5 points. curves U : 12 - t2 and Y = 12 - 6. 1. Find the area of the region enclosed by the (Hint: It might help to sketch the graphs) 12 - xt = X'- 6 \8 =2X' f,3-X So, "3 'i*o- f ' Q'-" ;= (x'-6 ) dx " J-3 rJ t. l-. -['(t -2x')/r J-3 rt :(\t ^ -tr') l-, -\' lz -x xLb YVb +': + " (-sq + 18 ) : (s+ - l8 )- : lol 4L :12

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2. Evaluate: I tunt o secs o d,o = J Un'0sec? *s,ro secl d0 l,et | =secf, = llecb -) sech'*n'no sqe {o +J,t" dt=*Ano seco /0 = IU'-l ) tq dt =It+t-+u)dt -t l -t

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4. Evaluate I,#* (Hint: factor the denominator first.) Xt++x = t (X't+) We wrtf,q )Xa-x+9 = + + BIt,' _ffi x' X.+4 we hourrx._x t+= A (xt+r+) +(Bx+c) x /' I I Elrrotrg u*\$vtents, w€ obtoin p-tB=2, Cr-l ' +A=q Thus [--l ,\$zl a^dc:-l ' Jo frr, LIq dx=16- J 1]+t+x t+)dx Texthok Ppe418 *an1Q S '/ft*x :Jg4dx + I+o' -fkd' +lldx ' ' x -6hlx{ +c - t lr' (xt* tt) - iorc{en<i
5. Determine whether the following integrals are convergent or divergent.

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MAC 2312 Exam 1 Spring 2011 Key - MAC 2312 Tpsr I Srnrxc...

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