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Unformatted text preview: APMA Ill Name Exam 2
March 31, 2008 Section Write and Sign the pledge: Directions: You must Show 3!] necessary work tojustjfy your answers. Solutions will be
graded for accuracy, completeness, and clariiy. No notes. books, calcuiators, or other
aids are permitted. Please circle your ﬁnal answer. ])(10 points) A 6inch thick aner of mulch is to be spread on a garden bed. The width
ofthe bed is measured every 2 feet as shown. All measurements are in feel. Use
Simpson’s rule to estimate the volume of mulch that is required. “' a.
$59: é?"SECLoWLﬁl'Lz—J'AF'LB+Q'L‘”F+$L5+LQ
t: 2 0+4._G+2.5+4"G‘+2‘2)*4“1403 v3 ’2.
(g HMMW’VQ . ‘—
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'25 :1 E; nkﬂg HEX
/,__J 2_) (20 points) Show whether each oflhe following integrals is convergent or divergent.
Ifeonvergent, evaluate the integral 3)(20 points) A tank is filled with water to a depth of2 m as shown. The vertical ends of
the tank are trapezoids with width6 m at the top and3 In at the bottom. The height of the
tank is 4 m, and the length is 7’ m as shown. I‘ﬁfbmﬂ tear—A a) Set up, BUT DO NOT EVALUATE, an integral to ﬁnd the hydrostatic force on one
vertical end ofthe tank. You must draw a sketch that illustrates your solution, and
identify the values ofany constants used, including the units. 13) Set up, BUT DO NOT EVALUATE, an integral to ﬁnd the work required to pump the '2)
water out of an outlet that is 1m above the top of the tank. You must draw a sketch that
illustrates your solution. and identify the values ofany constants used, including the units. __2 4) (20 points) Consider the curve x 21+ e’ , y = :2. 3) Find an equation for the line tangent to the curve at t = 2. b) For whﬁ va es oft is the curve concave up? $1“ f gar—J idemkt 9* 11166) (5‘? i eit’elb  >Oc=b1At>o comma up «Br £4 Ll c} Set up. BUT DO NOT EVALUATE. an integral to ﬁnd the length ofthe curve for
{} «1 r t? 3 i r____________.: 5
L ——— ix/Cﬁﬂtit Air—Vgime Ce O (1) Set up BUT DO NOT EVALUATE. an integral to ﬁnd the surface area generated by
rotating the curve For I) 3 z 3 3 around the y—axis. 3
5. == SWGaLéM/ﬁ't’HL 6% 5) (15 points) Find the area of the region within both of the cuwes with polar equations,
r = l, and r = 25in 1'9. Your solution must include a welliabeied sketch of the region. 6) (IS points) Find the coordinates of the centroid ofthe region bounded by the curves, y : \MX: and y: l.
I ﬂ ﬂ rz. — 2;  ‘*
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