# Disc5 - Math 21B Kouba Discussion Sheet 5 1 Use any method...

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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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