We’ll look at a few special-purpose methods later on. Volumes 52 2.3. Numerical Methods. Integration using Tables and CAS 39 1.9. u ′Substitution : The substitution u gx= ( )will convert (( )) ( ) ( ) ( ) b gb( ) a ga ∫∫f g x g x dx f u du= using du g x dx= ′( ). Improper Integrals 46 Chapter 2. More about Areas 50 2.2. Chapter 7: Applications of Integration Course 1S3, 2006–07 May 11, 2007 These are just summaries of the lecture notes, and few details are included. 1.5. 7.1 Remark. Numerical Integration 41 1.10. Integration by Parts: Knowing which function to call u and which to call dv takes some practice. Many other secondary techniques of integration are known, and in the past, these formed a large part of any second semester course in calculus. This is the most important theorem for integration. Partial Fractions 32 1.8. The aim here is to illustrate that integrals (definite integrals) have applications to … Most of what we include here is to be found in more detail in Anton. Arc Length, Parametric Curves 57 2.4. The fundamental theorem of calculus. Remark 1 We will demonstrate each of the techniques here by way of examples, but concentrating each time on what general aspects are present. method is integration by parts. Trigonometric Integrals and Trigonometric Substitutions 26 1.7. Here is a general guide: u Inverse Trig Function (sin ,arccos , 1 xxetc) Logarithmic Functions (log3 ,ln( 1),xx etc) Algebraic Functions (xx x3,5,1/, etc) Trig Functions (sin(5 ),tan( ),xxetc) This methods has a basis in the product rule of differentiation, and essentially, allows one to replace one (possibly hard) integral by another (hopefully simpler) one. Rules and methods for integration Math 121 Calculus II Spring 2015 We’ve covered the most important rules and methods for integration already. Ex. Standard Integration Techniques Note that at many schools all but the Substitution Rule tend to be taught in a Calculus II class. Integration by Parts 21 1.6. Applications of Integration 50 2.1. For indefinite integrals drop the limits of integration. Methods of Integration طــــــــــــــــــرق التــــــــــكامل February 2019 In book: حساب التكامل - Integral Calculus (pp.43-74)

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