INTEGRAL CALCULUS

By H. HIUNO

CONTENTS I THE QUESTIONS INTEGRATION DE?NITION OF THE INTEGRAL BASIC PROPERTIES OF THE DE?NITE INTEGRAL THE FUNDAMENTAL THEOREM OF CALCULUS SUBSTITUTION AREA BETWEEN CURVES VOLUMES INTEGRATION BY PARTS TRIGONOMETRIC INTEGRALS TRIGONOMETRIC SUBSTITUTION 1 10 PARTIAL FRACTIONS 1 11 NUMERICAL INTEGRATION 1 12 IMPROPER INTEGRALS 1 13 MORE INTEGRATION EXAMPLES APPLICATIONS OF INTEGRATION WORK AVERAGES CENTRE OF MASS AND TORQUE SEPARABLE DIFFERENTIAL EQUATIONS SEQUENCES AND SERIES SEQUENCES SERIES CONVERGENCE TESTS ABSOLUTE AND CONDITIONAL CONVERGENCE POWER SERIES TAYLOR SERIES II HINTS TO PROBLEMS PARTIAL FRACTIONS NUMERICAL INTEGRATION IMPROPER INTEGRALS MORE INTEGRATION EXAMPLES III ANSWERS TO PROBLEMS IV SOLUTIONS TO PROBLEMS