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Unformatted text preview: Math 17B
Discussion Sheet 3 1.) Use any method to determine the following indeﬁnite integrals (antiderivatives). a: e293 1+sina:
. ————d b. d . 5 d d. ——————
a)/ ._.__1_m2 1r )/1+e2x :r C) /COS w a: )/ c0823: drr e.) /(secx+seczx)d$ f.) /tan2:c seczmda: g.) /(—m%)_:$1-+—32dm h.) /(x2+1)(x3+3m)10d:r i.) /(—£+—6-dw j.) /(lnm)4 d9: 3134—5)2 :1: k.) /sec2(39:) 2mm“) dm 1.) + 3)\/;r —— de 2.) A three—dimensional solid object lies above the Cit-axis from m = 0 to :r = 4 centimeters.
The cross-sectional area of the solid taken perpendicular to the w-axis at a: is A(:z:) = 6m3
square centimeters. Compute the volume of the solid. 3.) Assume that snow is falling at the rate of t+ x/t in. / hr. at time t hours. Determine a
deﬁnite integral and compute the total amount of snowfall between t = 0 and t = 4 hours. 4.) Use a power u-substitution to integrate each of the following. a.) ‘/1‘+1\/Ed:r b.) /\/4+\/§dm c.) ﬁdm
3 5.) a.) The base of a solid lies in the region bounded by the graphs of y = 1 /;r, y = :r ,
and cc = 2. Find the volume of the solid if cross-sections taken perpendicular to the (Is—axis at a: are
i.) squares. ii.) rectangles of height 4. iii.) semi-circles. b.) The base of a solid lies in the region bounded by the graphs of y 2 ex, y = l, and
:1: : 3. Find the volume of the solid if cross-sections taken perpendicular to the m—axis at :r are
i.) triangles of height 5. ii.) equilateral triangles. 6.) Find the volume of the solid formed by revolving each region bounded by the given
graphs about the given axis. y = 1:2 — 1 and the :c—axis about the :r——axis
b.) y = ﬂ, y = 0, and .r 2 4 about the m—axis c.) y = ﬂ, y = 0, and a: = 4 about the y—axis d~) = 393, y = 6, and a: = 0 about the m—axis
e.) y = 230, y r: 5 —— (1/2)m, and y = 0 about the y—axis
f.) y=m2 andy=cc+2 about the 1iney=4
g.) y = $2 and y = 333 about the line y = 2
h.) = $2 and y = 2:3 about the line y = —1
i.) y = 9:2 and y = 1:3 about the line as = 3
j.) y = (1:2 and y = m3 about the line a: = —2
7.) Find the length of each graph on the given interval.
a.) y = $3” on the interval [0, 4] b.) y = (2/3)(m2 + 1)3/2 on the interval [0,2] 9:4 1
c. y = —4- + g; on the interval [2, 4] d.) y = (1/2)(e"’ + 6“) on the interval [0,1n2]
8.) Determine a function having the following properties :
f"(a:) = 1+ age/2,1010) = —1, and f(0) = 3 9.) Wildebeests (Gnus) are migratory animals and are an important part of the African
ecosystem, since their dung fertilizes the soil and their grazing and trampling encourage
new growth along migratory paths. Assume that a herd of wildebeests migrates along a 1
path given by y : (1/6)w3 + 51—; from at = 1 to m = 50 miles. Determine the total length
of this path. *********************************************************************** THE FOLLOWING PROBLEM IS FOR RECREATIONAL PURPOSES ONLY. 10.) Connect 6 toothpicks end-to—end to form 4 triangles. ...
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This note was uploaded on 02/17/2012 for the course MATH 17B taught by Professor Kouba during the Winter '07 term at UC Davis.
- Winter '07