4.4 - MA 160 Section 4.4 Worksheet Name 6 e v- 6» z 1* a...

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Unformatted text preview: MA 160 Section 4.4 Worksheet Name 6 e v- 6» z 1* a 34 Properties of Definite integral (Area and Average Value) Area Between Two Curves: Let f and g be continuous functions and suppose that fix) 3 g(X) over the interval [21, b]. Then the area ofthe region between the two Curves, from x = ate it = b, is jb[f(x) — g(x)]dx. Average Value: Let f be a continuous function over a closed interval [a, b]. The average value of f, yw, over [a, b] is given by ym‘ : b x+5, x<-1 f(x)={ wxz +x+6, xz—l --l 3 35(X+5idfi-PS(—'}L1+\(+é)dx b *l a (so _;\- (fig—-25) e («-3.— TZ+I9)—'(‘:|i'+‘ii'9i ‘—'- -L{,S' +IQ.-'5+ [3.5+ % 6’0 3 3. Given the curves f(x) = 2x+1 and g(x) = x2 +1. a. Find the points of intersection of the two curves. Xa-r I :: axe-l 1°“——2m::a PMJVQ XCx-fifl ~20 (a, i) m (c215) 1:0 w. 5L3)- . ‘3r—a curl-51 ‘333 9+1 (0, I) ‘3‘”; (2,55 b. Graph the curves and shade the region between the two curves. c. Find the area of the region between the two curves. Lag: 9““)“(1’Ze 0133c : a («21-— xLHw a )‘3 2- 51 are :da. 3' g )1- 1 a w%-o~;Lf‘—-g':__———Jg:_i 3- 3 6. Find the average value of the given function over the given interval. v :2 a. f(Jc)=16—x2 , [0, 4] : 3'70 Joe-£04; j: _‘:—£.1‘51‘;GHJ:L+ f_:_£’ f 00:6“ , [0,2] _ " ‘1 ->~ ‘ Q'ojp e cit“:- = flea—36%.; : q 3'." (8—1— 6°) 3 *-':('-'—,.~r\ _ __ l ‘ _ gel 1”: ‘6 I . {-‘Gidx bvq’ ‘(Q h : [1’6] x I C: (34.x:le jb—chlx. i :: 4%(hé—111X: ig-‘HLlé’ d. fgx)=x2+x+3 , [1,4] "1‘ 1 “f a . . 34V:q-.$ (X*K13)Cik:;[_—:—+L~+3x]) I i 3— .. { q ‘ "Efé-i—r 9+fl~§—:~3] :%[%—+QCD*? :J§[QI+AcHE-} :. .L-[Hli‘Qa—‘l H _L 75 _ .15 3 3.. _' 3 9. -' "7‘; 2 Answers for WS 4.4: 2 1. j1(—x2 +x+2)dx 2. ? 3a. (0, 1)and (2,5) 3b. 3c. 3 4.1.92—1 s. 13-41“ 3 2 2 6a. 2 6b. 21116307167 6c. 1— 1,:30.4323 6d. 35—2125 3 5 2 2e‘ 2 ...
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4.4 - MA 160 Section 4.4 Worksheet Name 6 e v- 6» z 1* a...

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