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Unformatted text preview: 16B CALCULUS
Francisco Santos Nov 16, 2007 Midterm 2, (odd numbered seats) Name: 2 Emot‘f‘ca gal"? HIM 1. ( 20 points) Evaluate the following five deﬁnite and indeﬁnite integrals. Simplify your
answers. SHOW your work. You may use usubstitution, trig formulas, the simple
power rule, the fundamental theorem of calculus, integration by parts, partial fraction decomposition, etc. Sim"; v~ c945 'Y Ma «K Mama aw a“ .. ..____‘.M,j (95 ‘vc' can “A Name: 2
c 3 41.4
“H?” dx = ———— .~~
C. f(7+sm:t) (4;, u: 79",ng 0/01 7: Colix'dx ......,__.._.—__...._~—_. 0 35—9 _ —,~;—;‘ ‘: * / “W. ’ .‘ ~"r/g ‘ IT/Z
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[6/u:¢l/;< (7.: 9m x " (,3, 9+ (0 yJ/QE .. ,..._.._._~._ Name: ID: 3 2. ( 8 points) Find the total area of the region bounded by the graphs of y = x —— 1 and
y = (:1:  1)3. Set up but DO NOT EVALUATE the integral(s). Name: ID: 4 3. (10 points) The outdoor temperature at time t hours is modelled by T(t) = 5545 cos (1350 — 3)). a. What is the temperature at ,_ . L 3pm and 9pm ( t = 15 and t = 21)? 5(27)'~55*‘/5 523:7? ‘67
L .5111
‘11 b. At what rate is the temperature changingTT' when t =5 hours? z“) 7.9/5 sam<g (JV 3) 42 .5 455;? SL'W(£ (4,3)) C/ T /(9 5 ﬂ fiim '71::9 , ‘ ,LT}I»1 g: 7/53;
‘1 c. What is the AVERAGE temperature between t = 9 and t = 21 hours? Name: ID' 4. (12 points) Consider the enclosed region R bounded by the graphs of y = ex, y = 82, z = 0. Set up but DO NOT EVALUATE the integral(s) which give the VOLUME of the solid
of revolution formed by revolving the region R around a. the xaxis ”“i ;.'i_ ““""'i'_j‘"+ b. the yaxis ...
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 Spring '11
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