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# AN GEOM & CALCULUS MATH 1552

LSU

GPA 3.72

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This 4 page Class Notes was uploaded by Madison Gottlieb Sr. on Tuesday October 13, 2015. The Class Notes belongs to MATH 1552 at Louisiana State University taught by Terrie White in Fall. Since its upload, it has received 16 views. For similar materials see /class/222627/math-1552-louisiana-state-university in Mathematics (M) at Louisiana State University.

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Date Created: 10/13/15

Common Derivatives and Integrals Derivatives Basic PropertiesFormulasRules cfx cf39x c is any constant fxigx39 f39xig39x icequot me n is any number c 0 c is any constant f g39 f39 g f g39 7 Product Rule 7Qu0tient Rule fg x f39g xg39x Chain Rule intrusive ltlngltxgtgtl gt Common Derivatives Polynomials in 0 in 1 cx c inquot an cxquot ncxH Trig Functions inn x cosx cosx sinx gum x secz x secx secxtanx cscx cscxcotx cotx ese2 x Inverse Trig Functions sin 1 x 1i x2 cos x 1 2 aban l x i d dx 560391 x dx lxlxlx2 1 ExgonentiaVLogarithm Functions axaxlna exex d 1 d 1 d 1 altlnx xgt0 alnxl x 0 5logax m xgt0 H lagerbolic Trig Functions iltsinh x cosh x iltcosh x sinh x ilttanh x sech2 x dx dx dx iltsech x sech xtanh x iltcsch x csch x coth x iltcoth x csch2 x dx dx dx Visit httgtutorialmathlamaredu for a complete set of Calculus l amp ll notes 2005 Paul Dawkins Common Derivatives and Integrals Integrals Basic PropertiesFormulasRules jcfxdxcjfxdxcisacoustant jfxrgxdxjfxdxjgxdx jfxdxFx Fb Fa where Fxjfxdx jjcfxdxcjfxdx cis aconstant jfxrgxdxjfxdxjgxdx jfxdxo jfxdx jfxdx b LfxdxJfxdxJfxdx Icdxcb a If fx2gx on 61Sbe then IfxdeJgxdx Common Integrals Polynomials Idxxc Ikdxkxc Ixquotdxxquotlc n 1 n1 Jidxlnxlc Ix39ldxlnxc Ix dx 1 x 1cn 1 x n1 1 1 E 1 51 q H J dx lnaxb c qudx xq c xq c axb a 1 pq Trig Functions Icosudusinuc Isinudu cosuc J seczudutanuc Isecutanudusecuc Icscucotudu cscuc Icsczudu cotuc Itanudulnsecuc Icotudulnsinuc Isecudulnlsecutanuc IsecSudusecutanu1nsecutanuc Icscudulncscu cotuc IcscSLidu cscucotulnlcscu cotuc ExgonentiaVLogarithm Functions 11 u u a Ie due c Ia dulnac Ilnuduulnu uc Ie sinbudumasinbu bcosbuc Iue duu 1e c mu 9 1 Ie cosbudua2b2acosbubsmbuc Jumudulnllnuc Visit httgtutorialmathlamaredu for a complete set of Calculus l amp ll notes 2005 Paul Dawkins Common Derivatives and Integrals Inverse Trig Functions l Talus1n4 Z c J sm39luduus1n 1uIl u2c a u a l l 1 u 1 1 1 2 2 2alu tan c Itan uduutan u lnlu c a u a a 2 dulsec4 Zjc Icos39luduucos391u l u2 c uxlu2 a2 a a H lggerbolic Trig Functions Isinhuducoshuc Icoshudusinhuc Isechzudutmhuc Isechtanhu du sechu c Icsch cothu du cschu c Icschz u du cothu c Itanhudu lncoshuc Isechudu tan 1 lsinhuc Miscellaneous J21 2duzilnua a u 2a c Jduiln u a uZ a2 2a 2 u a J czzu2 aluExlazu2 71nuxlazu2 c 2 u a I luZ az aluExlu2 a2 lnuu2 a2 c 2 u a u I aZ u2 aluExlaz u2 7s1n1 c a IVZau uz du uaI2au u2 a 22cos391a 2 u c Standard Integration Techniques Note that all but the rst one of these tend to be taught in a Calculus 11 class u Substitution Given Ibfgxg39xdx then the substitution u g x will convert this into the integral Ifg xg39xdx Ifu du Integration by Parts The standard formulas for integration by parts are b b Iudvuv Jvdu J udvuv J vdu Choose u and dv and then compute du by differentiating u and compute v by using the fact that v Idv Visit httgtutoriamathIamaredu for a complete set of Calculus amp notes 2005 Paul Dawkins Common Derivatives and Integrals Trig Substitutions If the integral contains the following root use the given substitution and formula laZ bzx2 3 x sin9 and cos29l sin29 Ibzx2 a2 3 x gsece and tan2 9 sec2 9 l Ia2b2x2 3 x tan9 and sec29 ltan29 b Partial Fractions P x Ifintegrating J QE 3 dx where the degree largest exponent of P x is smaller than the x degree of Q x then factor the denominator as completely as possible and find the partial fraction decomposition of the rational expression Integrate the partial fraction decomposition PFD For each factor inthe denominator we get terms in the decomposition according to the following table Factor in Qx Term in PFD I Factor in Qx Term in PFD A k LLmL axb axb axb axb axb2 axbk AxB k M WW WWW axzbxc Runway Products anal some Quotients of Trig Functions Isin x cos39 x dx 1 If n is odd Strip one sine out and convert the remaining sines to cosines using sin2 x 1 cos2 x then use the substitution u cos x 2 If m is odd Strip one cosine out and convert the remaining cosines to sines using cos2 x 1 sin2 x then use the substitution u sin x 3 Ifn and m are both odd Use either 1 or 2 4 If n and m are both even Use double angle formula for sine and or half angle formulas to reduce the integral into a form that can be integrated Itanquot xsec39quot xalx 1 If n is odd Strip one tangent and one secant out and convert the remaining tangents to secants using tan2 x sec2 x l then use the substitution u sec x 2 If m is even Strip two secants out and convert the remaining secants to tangents using secZ x ltanZ x then use the substitution u tan x 3 Ifn is odd and m is even Use either 1 or 2 4 If n is even and m is odd Each integral will be dealt with differently Convert Example cos6 x cos2 x3 1 sin2 x3 Visit httgtutorialmathlamaredu for a complete set of Calculus l amp ll notes 2005 Paul Dawkins

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