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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 2
Background image of page 3
This is the end of the preview. Sign up to access the rest of the document.

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 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) 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+5idfi-PS(β€”'}L1+\(+Γ©)dx b *l a (so _;\- (figβ€”-25) e (Β«-3.β€” TZ+I9)β€”'(β€˜:|i'+β€˜ii'9i β€˜β€”'- -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 1Β°β€œβ€”β€”2m::a PMJVQ XCx-fifl ~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€œβ€œ)β€œ(1’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_:_£’ f 00:6β€œ , [0,2] _ " β€˜1 ->~ β€˜ Q'ojp e citβ€œ:- = fleaβ€”36%.; : q 3'." (8β€”1β€” 6Β°) 3 *-':('-'β€”,.~r\ _ __ l β€˜ _ gel 1”: β€˜6 I . {-β€˜Gidx bvq’ β€˜(Q h : [1’6] x I C: (34.x:le jbβ€”chlx. i :: 4%(hΓ©β€”111X: ig-β€˜HLlé’ d. fgx)=x2+x+3 , [1,4] "1β€˜ 1 β€œf 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€œ 3 2 2 6a. 2 6b. 21116307167 6c. 1β€” 1,:30.4323 6d. 35β€”2125 3 5 2 2eβ€˜ 2 ...
View Full Document

{[ snackBarMessage ]}

Page1 / 3

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online