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Unformatted text preview: MA 1022 B ’08 Final Exam Name Instructions This test is closed book. Calculators are not allowed. Part I  Basic Skills Please Circle your Section A01 Heinricher, A (PLC) A02 Abraham,J (3:00)
IA04 Gold, V (8:00) A05 Teng, Z (9:00)
A07 Tashjian, G (1:00) A08 Malone, II (1:00) A10 Dai, s (10:00) All Dai, s (2:00) A06 Tashjian, G (9:00) A09 Blais, M (9:00) Part I — Basic Skills Work the following problems and write your answers in the space provided. Use the
scratch paper provided for your work. You need not simplify your answers. %/
IKE1+ E 249% C
1. J(x2+7\/x—15)dx Ans: 3 3 7(S/hn/K+ 035% ‘1‘" C
2. Ixcos(x)dx Ans: .J... m 5X “f” C
3. Isin4(x) cos(x)clx Ans: 5 9. ' Ans:A/;+e*)eﬁi x. grcﬂnfex) “g” C. 5. jedx Ans: ’23“
45" 6. (x2 +1)2 dx Ans: Ans, (67"){7QM a.) d
7. — 6”
dx( ) Part 11 Work all of the following problems. Show your work in the space provided. You
need not simplify your answers, but remember that on this part of the exam your
work and your explanations are graded, not just the ﬁnal answers 8. Find the area of the region between the curves y = x2 —. 4 and
y z x + 2. Include a welllabeled sketch of the region. 9W$€?§€PC’§7¢M ft: am 1‘3 : xgew‘ W" 2* (“a w» 2? 35” a + 2)
x: 3 cft K": “'1’” .3 3
F: Xszégwﬁm
“i E “'2 9. Let R be the region bounded by the curve y = x 2 +1 and by the lines
x = 1, x = 3 , and y = 0. Find the volume of the solid obtained by revolving R around the line y = —1. Include a welllabeled sketch of the region. 2
10. Consider the integral I (2x +1) dx and given that:
0 :13 : n(n +1)(2n +1) i=1 6 (a) Write a Riemann sum approximating the above integral by dividing the
interval of integration into 11 equal parts, and evaluating the function at the
_ right endpoints of the subintervals. I (b) Using the expression obtained in part (a), let n9 00 , and demonstrate
that the value of the integral as a limit of the Riemann sums is 6.  ff 6 i“;
. I 3 , I gives great {r 7% j 44 innpwruww 11. A11 empty cylindrical tank is 10 feet tall, has a 3 foot radius, and sits on a
pedestal that is 7 feet above the ground. How much work is required to
ﬁll this tank with oil that is currently at ground level? The oil’s density is
50 pounds per cubic foot. Assume that the ground level is where y=0. Set up the integral only, but do n_o_t perform the integration. 12. Compute the following integrals
3
—.7C
a. J. x26( )dx
. . spa. up  3/2 13. Compute the following (continues on next page): of ST" dt a. m dx 1—? 0 M;
.. a; a» ‘
:zﬁ g x; 9,7336%. :
3&5"  menma ' .1 \R.
mama” _ w 14. The element Strattonite has a halflife of 800 years. How much of a 1000
gram sample of Strattonite will remain after 150 years? You may express
your answer in terms of natural logarithms and/or exponentials. **** EndofExam “H ...
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 Spring '09
 Abraham
 Calculus

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