Unformatted text preview: Math 218 Kouba
Discussion Sheet 8 1.) Use any method to determine the following indeﬁnite integrals (antiderivatives). a) ——$i2——dx b) w+1 C) iii—dag
' x2+4x+5 $2+4x+5d ' $2+4x+3 d.) /se05:ctan3;rdm e.) /sec2:rtan2xd: f.) /(cot2:r + tan2 5:3)dac g.) /(sec3;r—csc(g))da: h.) /sin24zdm i.) /sin3xdx j.) fi?::d$ k.) /COs3xSln2$d£E l) fﬁdm 2.) Use partial fractions to integrate the following. 3:2 m+3
8” fay—1‘“ bl hm“
7—m2 1
09/de dl/xmdx 3.) Write the partial fractions decomposition for each. DO NOT SOLVE FOR THE UN
KNOWN CONSTANTS ! a) m2+7x5 b) 1
‘ (7932+3)2 172 (ac+3)3 ' x4+x2+1 4.) Use trig substitution to integrate the following.
1
2 3
a. a: \/1— 2‘da; b. / dx c. /m ~\/:r2—4dx
) / cc ) x\/:c2 + 9 ) 5.) A motor boat is resting at the origin, (0, 0), l)
and a skier, tethered to the boat with a 20—ft. rope, / °Q+
is resting at the point (20, 0). The boat then begins 7:4) #69
moving along the yaxis, pulling the skier along the S k Y‘
r t e
(X) 4309) unknown path, y = f (x) Use integration to ﬁnd
an equation for this path. “ I hear and I forget. I see and I remember. I do
and I understand.” Chinese Proverb ...
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 Spring '10
 KOUBA,DUANE

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