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Unformatted text preview: MAC 2233: Quiz 14 (Take —Home) SHORT ANSWER. Show all work CLEARLY in the space provided and write your answer on the i Find the integral. 2) f (2 + 2xjei4x + 2Mg) (13: u: *1"?le Anavex": Ex. 5.3 #55. Find The equoTion of The funeTion ﬁx) whose groph posses Through The given poinT. MAC 2233: Quiz 15 ULTIPLE CHOICE. Cheese the one alternative that best eempletes the statement or answers the qu nd the most general antiderivative.
1) I (2x3 — 7x + 2);:1}: 7—
A)t’ix2—?+C E)ﬁx4—14x2+2x+c 1 _, C}2x4—7x3+2x+C D}2X4—%X2+2){+C aluate the integral. 2)f2e93"1dx 7‘ 3.53ade A)%e9x+1 + C nd the derivative of y with respect to the independent variable. 3)~.:=8x 4' [7aﬁﬁ11,
J g b q
3 @sxlns A) 83": E) 83": In x C} x111 8 Find the derivative (If y with respect to x, t or 8, as appropriate.
4)}F=1n(x—6) 45' LEJ
. :: MEI [Ti—x Find the integral. _3_?
50f x dx
x
©4355—7111le C
_'.‘.r C)%x4— 7x3 +C Notation and Existence of the Definite Integral The symbol for the number I in the definition of the definite integral is o
/ ﬂat) tit which is read as “the integral from a to s of f of x dee x" or sometimes as “the integral
from o to is off of .r with respect to or." The component parts in the integral symbol also
have names: The function is the integrand. Upper limit of integration
/ Jr is the variable of integration. Integral sign EH Ea /
“sf ﬁx) dx
(:2 L . 1 t ft t / Whenyou ﬁnd the value
ﬂier “m D m Egm m W—J f of the integral, you have He“ P .
Integral 0f f lawn] a m b I etaluated the integral. NEE". 71a; Is. ﬂue TABLE 5.3 Rules satisﬁed by deﬁnite integrals a: b
1. Order effnfegreffen: cfx —/ ﬁx)a’x _.x[IL.[‘Lm11ig.~n
b a:
0 MW u [Ilehmmul 2. Zere HEM: Infervef.‘ / ﬁx) d; =
15 E1
3. CensfenfMefﬁpfe: / kﬁx) cx = I: ﬁx) dx ..xns'NLu11I:u;.1I1 ‘5 s
/ _f(.l‘) dx = —/ (35,; ﬂ. = _]
h s b
4. Sum and Differenee: / (ﬁx) i g(x)) dx = / ﬁx) dx i / g(x) six 15 e r:
5. Ae’a’iﬁvires / ﬁx) cfx + / ﬁx) dx = / ﬁx) dx
{1 b c: Fundamental Theorem, Part 2 (The Evaluation Theorem) We now come to the second part of the Fundamental Theorem of Calculus. This part describes how to evaluate definite integrals Without having to calculate limits of Riemann
surns. Instead we find and evaluate an antiderivative at the upper and losver limits of integration. THEOREM Er (Continued) The Fundamental Theorem of Calculus Part 2
If f is continuous at every point of [ca 3:] and F is any antiderivative of f on [an a]. then F fax) : a
/ f(.1‘) cfx = F05) — Fla). *ﬁh‘*hfvaﬁ'w Uu [Qizdﬁz t ght @ 2005 Pearson Education, Inc., publishing as Pearson AddisonWesley Ex. 5.4 (p. 354). Evaluu’re The definite inTegml. 203 31 ’l 5305.5: Hmk of n Raise Bounties! 82 Too Graph Suppose f ond g one Two eonTinuous funeTions on The closed inTenyol [o, b] sueh ThoT They do noT cross
oT ony poinT in The inTer‘yol. Then The oreo of The region bounded by The grophs of The funeTions is P‘ : Eben  jcviﬂgix given by: If The grophs of 1‘ end g (os desonibed oboye) cross in The inTeryol oT o poinT e beTween o ond b, Then The Aneo of The region bounded by The gnophs of The funeTions is given by: Six) Ex. 5.5 (p. 362) Find The: area of The region. Ex. 5.5 (p. 362) Find The area of The region.
4‘] int.) = (ﬁr 171’ 300 = 1'1 ...
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This note was uploaded on 02/15/2012 for the course MAC 2233 taught by Professor Staff during the Fall '10 term at Broward College.
 Fall '10
 Staff

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