# 4.4 - MA 160 Section 4.4 Worksheet Name 6 e v 6Β z 1 a 34...

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Unformatted text preview: MA 160 Section 4.4 Worksheet Name 6 e v- 6Β» 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 ο¬x) 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) β 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 ymβ : b x+5, x<-1 f(x)={ wxz +x+6, xzβl --l 3 35(X+5idο¬-PS(β'}L1+\(+Γ©)dx b *l a (so _;\- (ο¬gβ-25) e (Β«-3.β TZ+I9)β'(β:|i'+βii'9i ββ'- -L{,S' +IQ.-'5+ [3.5+ % 6β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 1Β°βββ2m::a PMJVQ XCx-ο¬ο¬ ~20 (a, i) m (c215) 1:0 w. 5L3)- . β3rβa curl-51 β333 9+1 (0, I) β3ββ; (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: 9ββ)β(1βZe 0133c : a (Β«21-β xLHw a )β3 2- 51 are :da. 3' g )1- 1 a w%-o~;Lfββ-g':__βββJg:_i 3- 3 6. Find the average value of the given function over the given interval. v :2 a. f(Jc)=16βx2 , [0, 4] : 3'70 Joe-Β£04; j: _β:βΒ£.1β51β;GHJ:L+ f_:_Β£β f 00:6β , [0,2] _ " β1 ->~ β Q'ojp e citβ:- = ο¬eaβ36%.; : q 3'." (8β1β 6Β°) 3 *-':('-'β,.~r\ _ __ l β _ gel 1β: β6 I . {-βGidx bvqβ β(Q h : [1β6] x I C: (34.x:le jbβchlx. i :: 4%(hΓ©β111X: ig-βHLlΓ©β d. fgx)=x2+x+3 , [1,4] "1β 1 βf a . . 34V:q-.\$ (X*K13)Cik:;[_β:β+L~+3x]) I i 3β .. { q β "EfΓ©-iβr 9+fl~Β§β:~3] :%[%β+QCD*? :JΒ§[QI+AcHE-} :. .L-[HliβQaββl H _L 75 _ .15 3 3.. _' 3 9. -' "7β; 2 Answers for WS 4.4: 2 1. j1(βx2 +x+2)dx 2. ? 3a. (0, 1)and (2,5) 3b. 3c. 3 4.1.92β1 s. 13-41β 3 2 2 6a. 2 6b. 21116307167 6c. 1β 1,:30.4323 6d. 35β2125 3 5 2 2eβ 2 ...
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4.4 - MA 160 Section 4.4 Worksheet Name 6 e v 6Β z 1 a 34...

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