LEADER 05333nam 2200649 a 450 001 9910141174603321 005 20191030193400.0 010 $a1-283-40084-7 010 $a9786613400840 010 $a1-118-13034-0 010 $a1-118-13033-2 010 $a1-118-13031-6 035 $a(CKB)2670000000133917 035 $a(EBL)818447 035 $a(OCoLC)768204532 035 $a(SSID)ssj0000570857 035 $a(PQKBManifestationID)11931381 035 $a(PQKBTitleCode)TC0000570857 035 $a(PQKBWorkID)10610847 035 $a(PQKB)10920637 035 $a(MiAaPQ)EBC818447 035 $a(Au-PeEL)EBL818447 035 $a(CaPaEBR)ebr10521397 035 $a(CaONFJC)MIL340084 035 $a(PPN)185060560 035 $a(EXLCZ)992670000000133917 100 $a20110516d2012 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 00$aIntroduction to integral calculus$b[electronic resource] $esystematic studies with engineering applications for beginners /$fUlrich L. Rohde ... [et al.] 210 $aHoboken, N.J. $cWiley$dc2012 215 $a1 online resource (430 p.) 300 $aDescription based upon print version of record. 311 $a1-118-11776-X 320 $aIncludes bibliographical references and index. 327 $aIntroduction to Integral Calculus: Systematic Studies with Engineering Applications for Beginners; CONTENTS; FOREWORD; PREFACE; BIOGRAPHIES; INTRODUCTION; ACKNOWLEDGMENT; 1 Antiderivative(s) [or Indefinite Integral(s)]; 1.1 Introduction; 1.2 Useful Symbols, Terms, and Phrases Frequently Needed; 1.3 Table(s) of Derivatives and their corresponding Integrals; 1.4 Integration of Certain Combinations of Functions; 1.5 Comparison Between the Operations of Differentiation and Integration; 2 Integration Using Trigonometric Identities; 2.1 Introduction 327 $a2.2 Some Important Integrals Involving sin x and cos x2.3 Integrals of the Form B;(dx/(asin x + b cosx)), where a, ? r; 3a Integration by Substitution: Change of Variable of Integration; 3a.1 Introduction; 3a.2 Generalized Power Rule; 3a.3 Theorem; 3a.4 To Evaluate Integrals of the Form B; a sin x + b cos x/c sin x + d cos x dx; where a, b, c, and d are constant; 3b Further Integration by Substitution: Additional Standard Integrals; 3b.1 Introduction; 3b.2 Special Cases of Integrals and Proof for Standard Integrals; 3b.3 Some New Integrals; 3b.4 Four More Standard Integrals 327 $a4a Integration by Parts 4a.1 Introduction; 4a.2 Obtaining the Rule for Integration by Parts; 4a.3 Helpful Pictures Connecting Inverse Trigonometric Functions with Ordinary Trigonometric Functions; 4a.4 Rule for Proper Choice of First Function; 4b Further Integration by Parts: Where the Given Integral Reappears on Right-Hand Side; 4b.1 Introduction; 4b.2 An Important Result: A Corollary to Integration by Parts; 4b.3 Application of the Corollary to Integration by Parts to Integrals that cannot be Solved Otherwise; 4b.4 Simpler Method(s) for Evaluating Standard Integrals 327 $a4b.5 To Evaluate x2 + bx + cdx5 Preparation for the Definite Integral: The Concept of Area; 5.1 Introduction; 5.2 Preparation for the Definite Integral; 5.3 The Definite Integral as an Area; 5.4 Definition of Area in Terms of the Definite Integral; 5.5 Riemann Sums and the Analytical Definition of the Definite Integral; 6a The Fundamental Theorems of Calculus; 6a.1 Introduction; 6a.2 Definite Integrals; 6a.3 The Area of Function A(x); 6a.4 Statement and Proof of the Second Fundamental Theorem of Calculus; 6a.5 Differentiating a Definite Integral with Respect to a Variable Upper Limit 327 $a6b The Integral Function x1 1/ t dt, (x > 0) Identified as ln x or logex 6b.1 Introduction; 6b.2 Definition of Natural Logarithmic Function; 6b.3 The Calculus of ln x; 6b.4 The Graph of the Natural Logarithmic Function ln x; 6b.5 The Natural Exponential Function [exp(x) or ex]; 7a Methods for Evaluating Definite Integrals; 7a.1 Introduction; 7a.2 The Rule for Evaluating Definite Integrals; 7a.3 Some Rules (Theorems) for Evaluation of Definite Integrals; 7a.4 Method of Integration by Parts in Definite Integrals; 7b Some Important Properties of Definite Integrals; 7b.1 Introduction 327 $a7b.2 Some Important Properties of Definite Integrals 330 $aAn accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciences Integration is an important function of calculus, and Introduction to Integral Calculus combines fundamental concepts with scientific problems to develop intuition and skills for solving mathematical problems related to engineering and the physical sciences. The authors provide a solid introduction to integral calculus and feature applications of integration, solutions of differential equations, and evaluation methods. With logical organization coup 606 $aCalculus, Integral$vTextbooks 615 0$aCalculus, Integral 676 $a515/.43 686 $aSK 400$2rvk 701 $aRohde$b Ulrich L$0728646 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910141174603321 996 $aIntroduction to integral calculus$92103164 997 $aUNINA