Unformatted text preview: Math 21B
Kouba
Discussion Sheet 5 1.) Use any method to determine the following indeﬁnite integrals (antiderivatives). e“: 62’: ex 6": + 1
a. d b. d . d d. ——d
)/e$+1$ )/6w+1$ C)/e2$+1m )/a:e"””+1$
) fsecasdrc f.) /sec:rtan:rda: g.) /sec2mtan:rd:r h.) /sec5:rtanmdm
)/sec5.rtan3a:da: j.) /sec2:rtan2:rda: k.) /(cot2:r+tan2 5x)da:
l.)(:/(sec3;r—csc (—))da: 111.) /sin2 4:1:dw n.) /sin31:dzr o.) /cos3:rsin2;rdm
94 1d 1 2 3
p)/co $+ q.) / . d2: r.) /sec xdm 8) /sec mdm
cot 4.2: smwcosa: tang: tans:
1 1
. —~— . V1 . —~—d
tft/anarda: ud)/1+cos:rdac V)/ +$dx W )/\/1+~332 a: X./ \/1+x2d:r y.)/\/1+\/md:r z.) ﬁrm 2.) Use partial fractions to integrate the following. 11:2 m+3
3“ /m2_1d$2 Mfr—197m“
7~$ 1
C‘) fwd d> /r3+1d$ 3.) Write the partial fractions decomposition for each. DO NOT SOLVE FOR THE
UNKNOWN CONSTANTS I x2+7a3—5 1 . —————— b. —~—~—
a) (7102+3)2 11:2 (x+3)3 ) $4+$2+1 4.) Find a function 5(12) with the following two properties : S'(:r) = 6x2 + a: and
S (3) 2 5 . HINT : Use the First Fundamental Theorem of Calculus (FTCI). 3 2
5.) Assume that f is an odd function with / f(:c)d:1: : 7 and f(x) dd: 2 4 . Find the
1 ‘1
3
value of/ 6f(3:)d$
2 THE FOLLOWING PROBLEM IS FOR RECREATIONAL PURPOSES ONLY. 6.) A nonnegative integer I is a perfect square, triangular (PST) number ifI is equal to the
square of a nonnegative integer AND is also equal to one—half the product of consecutive
nonnegative integers. Find the ﬁrst four PST numbers. ...
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 Winter '09
 Kouba
 Calculus

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