Table of Integrals, Series, and Products Seventh Edition. Table of Integrals, Series, and Products Seventh Edition I.S. Gradshteyn and I.M. Ryzhik The Order of Presentation of the Formulas xxvii Use of the Tables xxxi Index of Special Functions xxxix Notation xliii Note on the Bibliographic References xlvii 104 Comparison of Formulas for Rectangular, Polar and Parametric Forms 105 Area of a Surface of Revolution 106 Volumes of Solids of Revolution Chapter 9: Improper Integrals 112 Definite Integrals with Infinite Limits of Integration 113 Definite Integrals with Discontinuous Integrands Version 4.7 Page 4 of 236 January 1, 2020 Equation of a plane A point r (x, y, z)is on a plane if either (a) r bd= jdj, where d is the normal from the origin to the plane, or (b) x X + y Y + z Z = 1 where X,Y, Z are the intercepts on the axes. Vector product A B = n jAjjBjsin , where is the angle between the vectors and n is a unit vector normal to the plane containing A and B in the direction for which A, B, n form a right-handed set Common Derivatives and Integrals decomposition according to the following table. Factor in Qx( ) Term in P.F.D Factor in Qx( ) Term in P.F.D ax b+ A ax b+ ax b(+)k ( ) ( ) 12 2 k k AA A formulas to reduce the integral into a form that can be integrated.

## Calculus I Formulas. MAC 2311. 1. Limits and Derivatives. 2. Differentiation rules. 3. Applications of Differentiation. 4. Integrals. 5. Applications of Integration.

©2005 BE Shapiro Page 3 This document may not be reproduced, posted or published without permission. The copyright holder makes no representation about the accuracy, correctness, or Basic Integration Formulas and the Substitution Rule 1The second fundamental theorem of integral calculus Recall fromthe last lecture the second fundamental theorem ofintegral calculus. Theorem Let f(x) be a continuous function on the interval [a,b]. Let F(x) be any Title: Integration Tables from Stewart Calculus Textbook 4th Ed. Created Date: 8/22/2011 7:22:05 PM Integration formulas y D A B x C= + −sin ( ) A is amplitude B is the affect on the period (stretch or shrink) C is vertical shift (left/right) and D is horizontal shift (up/down) Limits: 0 0 sin sin 1 cos lim 1 lim 0 lim 0 Integral Calculus Formula Sheet Derivative Rules: 0 d c dx nn 1 d xnx dx sin cos d x x dx sec sec tan d x xx dx tan sec2 d x x dx cos sin d x x dx csc csc cot d x xx dx cot csc2 d x x dx d aaaxxln dx d eex x dx dd cf x c f x dx dx