Calculus
Textbooks
Boundless Calculus
Inverse Functions and Advanced Integration
Calculus Textbooks Boundless Calculus Inverse Functions and Advanced Integration
Calculus Textbooks Boundless Calculus
Calculus Textbooks
Calculus

Section 2

Techniques of Integration

Book Version 1
By Boundless
Boundless Calculus
Calculus
by Boundless
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9 concepts
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Basic Integration Principles

Integration is the process of finding the region bounded by a function; this process makes use of several important properties.

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Integration By Parts

Integration by parts is a way of integrating complex functions by breaking them down into separate parts and integrating them individually.

Trigonometric Integrals

The trigonometric integrals are a specific set of functions used to simplify complex mathematical expressions in order to evaluate them.

Trigonometric Substitution

Trigonometric functions can be substituted for other expressions to change the form of integrands and simplify the integration.

The Method of Partial Fractions

Partial fraction expansions provide an approach to integrating a general rational function.

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Integration Using Tables and Computers

Tables of known integrals or computer programs are commonly used for integration.

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Approximate Integration

The trapezoidal rule (also known as the trapezoid rule or trapezium rule) is a technique for approximating the definite integral $\int_{a}^{b} f(x)\, dx$.

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Improper Integrals

An Improper integral is the limit of a definite integral as an endpoint of the integral interval approaches either a real number or $\infty$ or $-\infty$.

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Numerical Integration

Numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral.

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