Disc4 - Math 218 Kouba Discussion Sheet 4 1 Use any method...

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Unformatted text preview: Math 218 Kouba Discussion Sheet 4 1.) Use any method to determine the following indefinite integrals (antiderivatives). a.) /arcsinxd$ b.~——)/ COSCE CJ/lnwdmd . x(ln$)2d$ l+sin2 33d (lnzc)2 / 3+lna: x+1 . d f. ——d ———d h‘ ————d e)/ :17 LE ) :1:(4+ln:v) 1c mg)/(4:lc+3)3) a: ) (4a:+3)3 m :1:+2 a: 1 '. ——————d '. _— . —~—~ l)/$2+4a:+13 ’3 J)/m2+4m+13d$ k)/25$2+9dw 71: 1:2 513+5 1+:c6 l. ——d . d . ————————~d . d )/25$2+9 a: m)/$2+1$ n)/2:132+3:1:+5 x 0)/ :135 m )/ “:5 d )/ “32 d r.) 1‘35 :1:s.)/(4 +3)—3—d:c . :L' . [E {I} p 1+2:6 q 1+$6 x/l—4x2d 2.) Compute the area of the region bounded by the graphs of y : 336:”, y = 0, and m : ln4 3.) Find the following antiderivative two ways, using u—substitution and using integration by parts: /m5(1 + m3)4 d2: 4.) Find the following antiderivative by using integration by parts twice, then using alge— braic manipulation : /e2z sinxdzv 5.) Find the average value of f(m) : mlna: 0n the interval [1,6] . THE FOLLOWING PROBLEM IS FOR RECREATIONAL PURPOSES ONLY. 6.) Determine the exact value of the following expression : \/1+\/1+\/1+W ...
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