10_4notesDONE.pdf - CachC10_4notes 10.4 Area& Lengths in...

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Unformatted text preview: CachC10_4notes 10.4 Area & Lengths in Polar Coordinates Warm-Up The length. of the curve determined by x = 32‘ and y = from t: 0 to t: 9 is A) Lfl/Qtfiztfidt Bj [:62 9—416ridr 0L: x/9+16t d: D) J03J9~16r2dt E)! «/9+16t A Elk ,) CH m r." we. ( At 3 A: ll “’1 SJ 0} Nee?“ CW 0 We want to find the area inside a length of are. We cut the length into little pieces and add them. “54’ Rel/mean bore? length: I dx2 + dyg— 2d): dx dt =I 1+[%]2dx :J‘ [%]2+[%]Zdt CachC10m4notes Nowwe want d6: 1:! 63,362+ dyz d6 3:: recs!) y=rsin19 -:'—‘=—rsin19+%cosc9 (Wadi-m 11113) » [m—~rsinfl+—cosfl] air [d—6]=r sin 19— —2‘sEn8cosf)%+ [d0] cos 8 £11: rc056+ gaina I [%=rcos€+:—;sin8] [5%]! =r cos B+2rsi1n9cos€%+[:—;-]z sin .9 Wawantdfl I I add 3 + 35!. d3 d3 _ I r’sh’fl—erinflcosHj—g+[§L] 1:051!) 1 1 . dr 1 . 3 + 1" cos 3+2rsu13c050—+ — sin 9 d9 1 I rls‘zn‘fiH rimszfli- £- sin'6‘+ i @0520 d1? d9 H(sin’3+ cm’B) + d—r I{Slinléihzns’ii'} d3 dr 2 #1:} {a} (I) 1:; r1+[§;]1 d8 CachC10_4notes >< .: VC 03 B 7:: \l rs”; (.3 ex. r=sin2£9 0:16:2- "a1: 2cos 26’ d6 1:!”14 /sin2 29+ 4003226 (276? Calculator does not need % -_ 0 . . to be in polar form Area Remember how to find the area of a sector: CachC10_4notes p. 674 2. Find the/afi[email protected] the region that is bounded by the given curve and lies Me specified sector. r=e§f2 @59327r 2 31? ”fig (6%) AB 3‘ ”Jig @949 Cu- Q‘QS LI 4% m0)" 8. Find the aiegfof the filaded region. A; fig (Smblojzd B r : sin 46? ‘4 '" “‘2; TT .” “LEM (a) M Q)» ”a 25(p.1’16q {36f .’ {Vi—A" u “h“ _CachC10_4notes l3. Sketch the curve and find the area that it encloses. 7'24—sin9 , 1r? / w ‘5 "gm (Ll-“gm e) A (9* _ ”agrees- -— A q 0- Sumo 22. Find the area of the region enclosed by one loop of the curve. 7' 2 2+ 30036 M,_,_ > ( ' 2+5Lus 6) 1 O lnner ‘06? C058; ”3:; CachC10_4notes I 28. Find the area of the region that lies inside the first curve and outside the second curve. ( ' ”“31 F: iii” (9 I I O: H‘L‘NG O I 30.35 0 “.1 [email protected] Circa-56 9v'fi a.- ”$13"? “‘T It \ 2, l 2 (a 9316‘ g 2 Z (|+L0§®)J0 h“ 2 TV C03 38. Find all points of intersection of the given curves. r=2, . r=200326 '2 1: ZCQS ZG \ I: CoQ-Q 2'9; 0 J 2'“) LtTi”) L.«—- .4 2:;‘1952—6 8: (3)113 2n).._ W‘ ““29" 29 '3 “WI 311" 911" ,,- } ) 931?? 33;? 53%“ [2,11’) (:2 3F ’ 2*) ZJ‘ CachC10_4notes I 91;" w ow .1 «3g 1 1,, 1 47. Find the length of the polar curve. 01.," r=235 0S6S2fl,‘ A9'5’rlnlw \ 3 L1 , Ci 5 H dye 51. Use a calculatOI 01 compute1 to find the length of the loop i f” G ‘-‘-‘ ““" 2 $ \ A 16) oouect to four decimal places. M» / One loop of the four—leaved rose 7‘ : cos 2&9 ” (9 2 rr 4T “1: 0 4 /_ TT . - I . , “a _ 8- S' \chm'a.,_€fil 1+ (—25%.«263 dg ...
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