Advanced Engineering Mathematics, 7th Edition

APPENDIX A

Integral-Defined Functions

INTRODUCTION

Many important functions encountered in applied mathematics are defined in terms of an integral. There are several ways of doing this. In Sections 1.1, 2.3, and 3.2, we have already seen that a solution of a differential equation may lead to a function of the form

(1)

In calculus, you may have seen that one definition of the natural logarithm is given in terms of an integral of the form given in (1):

An integral-defined function can also be of the form

(2)

where it is understood that x is ...