# Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 15

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## Murray R. Spiegel:

## Murray R. Spiegel: *Mathematical Handbook of Formulas and Tables: Chapter 15*

Published $1968$.

## $15 \quad$ Definite Integrals

### Definition of a Definite Integral

### General Formulas involving Definite Integrals

### Leibnitz's Rule for Differentiation of Integrals

### Approximate Formulas for Definite Integrals

### Definite Integrals involving Rational or Irrational Expressions

### Definite Integrals involving Trigonometric Functions

- $15.29$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\sin^2 x$ and $\cos^2 x$

- $15.30$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\sin^{2 n} x$ and $\cos^{2 n} x$

- $15.31$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\sin^{2 n + 1} x$ and $\cos^{2 n + 1} x$

- $15.46$: Definite Integral from 0 to $2 \pi$ of $\dfrac 1 {\paren {a + b \sin x}^2}$ and $\dfrac 1 {\paren {a + b \cos x}^2}$

- $15.50$: Definite Integral to Infinity of $\sin a x^2$ and $\cos a x^2$

- $15.53$: Definite Integral to Infinity of $\dfrac {\sin x} {\sqrt x}$ and $\dfrac {\cos x} {\sqrt x}$

### Definite Integrals involving Exponential Functions

### Definite Integrals involving Logarithmic Functions

- $15.102$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\map \ln {\sin x}$ and $\map \ln {\cos x}$

- $15.103$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\paren {\map \ln {\sin x}}^2$ and $\paren {\map \ln {\cos x}}^2$

- $15.106$: Definite Integral from $0$ to $2 \pi$ of $\map \ln {a + b \sin x}$ and $\map \ln {a + b \cos x}$

### Definite Integrals involving Hyperbolic Functions