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**Unformatted text preview: **MA 160 Section 4.2 Worksheet Name C; a. r— Go :4! +0 5
Area, Antiderivatives, and Integrals Basic Integration Formulas Integral Rules WWFWx 2. fxrdx = xrﬂ H1 + C , provided r at -1 Rule B. f[f(x) i g(x)]dx = IKIMJC i 1.9005!" 15 Find the function ﬁx) with the properties: f’(31c)=‘%8x3 and f(l)=4.
“6‘: Hooch: f8x“34x__ 83- X ’3 W: 6/3
. .3}. ___ Mae(l,‘f}xiw-¥Ck):é>¢wg+cl§ - “(3 ”=6“! +C H=6+C m
”a": C— M¥(K)—-éx ‘2 16. Find the function ﬁx) with the properties: f (x): 4e“ and f (0)— _ 1—3. $(x):j$‘(x)cix:f‘{es dx:.‘ft"3f,—€3:C= i833x+c
3 MermlJt(Q,I §)m+(}c}:w’€” +C$MC§ L9. ._ 4 31 3 '
1'0 _ _
“-3" - :3? t C “'3'“ - C
A 2'- C- «40' r
17] A company determines that the marginal cost of producing the xth unit of a produ 15 C ’(x) = x3 - 2x . Find the total cost function, C, assuming that C(x) is in dollars and that ﬁxed costs are
$6000. C(X):f(xg*2x)dki 2:!" ﬁlm; +C:_ q ‘— (.300
I _ l 2.
M' 66‘)“ q'x ”X +6000
Answers
1 —3x+C 2. —x +C 3. +C 4. ——x3+C 5. ln|x|+C 6. —2+C
2 5x 4 2x
4
7 ——1n|x|+C 8 _12+C 9. ixsm3x6+lx —§x- +9x+C 10. 4+3): +C
14x 8 3 4 2 4x 4
5 4
11. 9 e5’+C 12. Jae—Sue 13. §e°-*‘+~2—x +C 14. 5x +—l—e'S —71n|x|+C
5 s 2 5 3
1 ' 4 1
15. f(x)=6x3—2 16. f(x)=—e“+ 17. C(x)=—x4—x2+6000 4 ...

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