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Unformatted text preview: Math 21B
Kouba
Discussion Sheet 10 . 1
1.) Consider the region R lying below the graph of y = — and above the x—axis on the interval x
[1,00) .
a.) Determine if R has ﬁnite or inﬁnite area.
b.) Form a solid by revolving R about the x—axis. Determine if the resulting volume is ﬁnite or inﬁnite.
c.) Form a solid by revolving R about the yaxis. Determine if the resulting volume is
ﬁnite or inﬁnite. 2.) Compute the following imprOper integrals. oo 1 0 3m 00 1 1 00
\/§ 1 82+]. 7 e 2
d.) —oox2+9 d1: e.)/1 131 do: f.)/0 a: lnzc dx °° 1 5 1 °° 24
. h. __ 3 ________
g) ./2 SCUM? d2: ) [0 «25—952 do: I) /1 2$2+5m+2 d9” 5 8:6 00 3 7r/2
j.) / dm k.) / 1:26z d1: 1.) / cscxcotzz: d3:
0 $2 ‘ 9 — o 00 oo oo 1 1 00 6—1/2.
m.) / ace—5”” da: n.) / —2 dac o.) / Ina: da: p.) / 2 d1:
0 o a: o 0 13 3.) Use the Comparison Test to show that the following improper integral converges, i.e., is co
1
————— dx
/1 Vm3+16 4.) Use the Comparison Test to show that the following improper integral diverges, i.e., is
°° a: + 4 ———— d1:
1 V$3+16 5.) Find the slope of the line tangent to each graph at the given value of 6. ﬁnite : inﬁnite : a.) r=2+cost9 for 0:37r/4
b.) r=4sin0 for 0:7r/3 c.) r=9+1 for 0:71" 6.) Find the area of the region bounded by the graphs of 0 : 1r/ 6 , 6 = 7r /4 , and r = sec 0 . 7.) Find the area of the region lying inside the graph of 'r = 2 + sinl‘} and outside the graph
of r = c056 . 8.) Find the area of the region shared by the circles r = x/gsinél and 7‘ = 0059 . 9.) Find the area of the region lying inside the graph of 7' = 4sin0 and above the line
7‘ = 0800 . “Deal with the faults of others as gently as with your own.”— Chinese Proverb ...
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 Spring '10
 KOUBA,DUANE

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