Test Key #2 - =~=~=~-~ 3/qjzct L MATH 150B Calculus II...

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--·====================~==~~~~~~~~~~==============~------------~ 3/qjzct L MATH 150B Calculus II Review Test# 2 Name K~ 1. Find the area of the region bounded by the following 2. Let a> 0 and b > 0. Show that the area of the ellipse equations by integrating (20 pts) ..,_ j __ f. ~ x2 y2 } a2 + b2 = 1 is nab. (15 pts) X = 4 -/; X = y-2 4 ° b 3. I (a) with respect to x: A = JJJ(x)-g(x)~~ _; . d I) -'t (b) with respect toy: A= f [f(y)-g(y)]dy ~ 3 c ~-~ (c) which method is simpler? Why? ~ J::Xt2. lt.to ~\1\~ec~:etA-erv\. 1l-olvd>: (-S>-3)/ (()1 2.) ") () . s4 .-A= ~ [9c.tz)- ( -J4-x >J~x t 0 (H-){ -(-J-t--7( )] ~;( ..-s--~~ (xtJ~~:x-r-z)cb<+ ~ )o'\r4-x Gtt 3 0 3 4 ~ C-t 'l.;. ·s (4-XY-t-"x 1,5+ ;;... (-;) (4-XJ"i Jo 6 l g "L \z.S :::Tt--"3::::: :6· If 't. . L~ ) A = ) ~ +-~ ~ l~ -2.) 1 d * -3 ~ 5_: c -'}2.-~ tb) ~~ 2. -;:; - t t~3-t~ ij~..:..b ~ J -.5 (C) ~ Page 1 of 5 1kP-<(r~ ~1J ~-el\ l~s.e ~\iei.AI> ~~tit -\W_ fl\ (~ 6{) -\W ---f,---"---&--"-{)-t--...:..J.-J.--L_....~:::{ ~u · 'f!.rc '~ '1\,L~ ~1\J:~J. 1\1. ~ 4 ~ (A.tt J.\f"C\ Ill +-. w-e 6-vlt~ 11 ~ -\-o -¥--~~ 4tA-L ~ ~ll'tJ (~"J-. r (\ iP ·~ A -=-)0 o:Jet~-x'L cl~ \...oolc:~ ~ut \-~ "(v\, -\1 0"1 --r~ Y.e ~.\ \c~~ 1= ..k_ .. ~ (xlcl-'1('1. t 0..2. arcSin;_~ (\
~:---=~-~--==========~~~=====================-------~ MATH 150B Calculus II Review Test# 2 Name \(<2-~ 3. Setup and evaluate the integral that gives the volume of 4. The arc of y = 4-( x2 I 4) on the interval [0, 4] is the solid formed by revolving the region about the x-axis. revolved about the line y =b. (20 pts) '---(15 pts) ~ f:. h 2 (a) Use Disk Method: V = 1r L [ R ( x) J dx, find y=x2, y=xs 1''1~xr l •0 )< ~.:"')t.t.. c ·t (7 0 0 1!•0 () l !.

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